a dissipative particle dynamics method for arbitrarily complex geometries dissipative particle dynamics dpd is an effective lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries here we formulate a local detection method for dpd involving arbitrarily shaped geometric three dimensional domains by introducing an indicator variable of boundary volume fraction bvf for each fluid particle the boundary of arbitrary shape objects is detected on the fly for the moving fluid particles using only the local particle configuration therefore this approach eliminates the need of an analytical description of the boundary and geometry of objects in dpd simulations and makes it possible to load the geometry of a system directly from experimental images or computer aided designs drawings more specifically the bvf of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance wall penetration is inferred from the value of the bvf and prevented by a predictor corrector algorithm the no slip boundary condition is achieved by employing effective dissipative coefficients for liquid solid interactions quantitative evaluations of the new method are performed for the plane poiseuille flow the plane couette flow and the wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and high order spectral element solution of the navier stokes equations we verify that the proposed method yields correct no slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface moreover we construct a very complex 3d geometry the brown pacman microfluidic device to explicitly demonstrate how to construct a dpd system with complex geometry directly from loading a graphical image subsequently we simulate the flow of a surfactant solution through this complex microfluidic device using the new method its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration in addition to stationary arbitrary shape objects the new method is particularly useful for problems involving moving and deformable boundaries because it only uses local information of neighboring particles and satisfies the desired boundary conditions on the fly

feedback control for fractional impulsive evolution systems this paper is mainly concerned with feedback control systems governed by fractional impulsive evolution equations involving riemann liouville derivatives in reflexive banach spaces we firstly give an existence and uniqueness result of mild solutions for the equations by applying the banach s fixed point theorem next by using the filippove theorem and the cesari property a new set of sufficient assumptions are formulated to guarantee the existence result of feasible pairs we also present an existence result of optimal control pairs for the lagrange problem

on the concept of general solution for impulsive differential equations of fractional order q 1 2 in this paper we provide the formulas of general solution for some impulsive differential equations of fractional order q 1 2

stabilization of a coupled transport diffusion system with boundary input we consider the problem of stabilizing a coupled transport diffusion system with boundary input the system is described by two linear transport diffusion equations and is not asymptotically stable in order to stabilize the system with boundary input sensor influence functions are assumed to be located at interior of the domain first we formulate the system as an evolution equation with unbounded output operators in a hilbert space using variable transformation next we derive a reduced order model with a finite dimensional state variable for the infinite dimensional system then a stabilizing controller is constructed for the reduced order model under an additional assumption it is shown that the finite dimensional controller together with a residual mode filter plays a role of a finite dimensional stabilizing controller for the original infinite dimensional system if the order of the residual mode filter is chosen sufficiently large finally the validity of the design method is demonstrated through a numerical simulation

on nonlinear conservation laws with a nonlocal diffusion term abstract scalar one dimensional conservation laws with a nonlocal diffusion term corresponding to a riesz feller differential operator are considered solvability results for the cauchy problem in l are adapted from the case of a fractional derivative with homogeneous symbol the main interest of this work is the investigation of smooth shock profiles in the case of a genuinely nonlinear smooth flux function we prove the existence of such travelling waves which are monotone and satisfy the standard entropy condition moreover the dynamic nonlinear stability of the travelling waves under small perturbations is proven similarly to the case of the standard diffusive regularisation by constructing a lyapunov functional

numerical investigation of microfluidic sorting of microtissues we characterize through simulation a microfluidic based particle sorting approach instrumental in flow cytometry for quantifying microtissue features the microtissues are represented herein as rigid spheres the numerical solution employed draws on a lagrangian lagrangian ll smoothed particle hydrodynamics sph approach for the simulation of the coupled fluid rigid body dynamics the study sets out to first quantify the influence of the discretization resolution numerical integration step size and sph marker spacing on the accuracy of the numerical solution by considering the particle motion through the microfluidic device we report particle surface stresses in the range of 0 1 1 0 pa i e significantly lower than the critical value of 100 pa that would affect cell viability lift off of non neutrally buoyant particles in a rectangular channel flow at the target flow regime is investigated to gauge whether the particle shear stress is magnified as a result of dragging on the wall several channel designs are considered to assess the effect of channel shape on the performance of the particle sorting device moreover it is shown that a deviation in flow rate does not influence the focusing of the particles at the channel outlet

the proof of a conjecture on the lewin number of primitive non powerful signed digraphs abstract suppose s is a primitive non powerful signed digraph a pair of sssd walks of s are two directed walks of s which have the same initial vertex same terminal vertex and same length but different signs the lewin number of s denoted l s is the least positive integer k such that there are both sssd walks of lengths k and k 1 from some vertex u to some vertex v possibly u again of s this paper presents a proof of a conjecture on l s which was put forward by you et al l h you m h liu b l liu bounds on the lewin number for primitive non powerful signed digraphs acta math appl sinica 35 2012 396 407

existence of mild solution for evolution equation with hilfer fractional derivative the paper is concerned with existence of mild solution of evolution equation with hilfer fractional derivative which generalized the famous riemann liouville fractional derivative by noncompact measure method we obtain some sufficient conditions to ensure the existence of mild solution our results are new and more general to known results

on a problem of lewin abstract a digraph g is called primitive if for some positive integer k there is a walk of length exactly k from each vertex u to each vertex v possibly u again if g is primitive the smallest such k is called the exponent of g denoted by exp g in 1971 m lewin introduced the paramater l g for a primitive digraph g it is the smallest k for which there is both a walk of length k and a walk of length k 1 from some vertex u to some vertex v possibly u again clearly l g exp g and so l g n2 2n 2 by a theorem of wielandt finer upper bounds on l g are given and an open problem is presented

analysis of time fractional and space nonlocal stochastic incompressible navier stokes equation driven by white noise abstract in this paper we consider the stochastic time space fractional incompressible navier stokes equation driven by white noise we firstly derive the regularity of the nonlocal stochastic convolution then we prove the global existence and uniqueness of the mild solution finally the holder continuity for the stochastic time space fractional incompressible navier stokes equation driven by white noise is established the optimal holder continuity accords with the result of integer order time incompressible navier stokes equation

splitting methods for the nonlocal fowler equation we consider a nonlocal scalar conservation law proposed by andrew c fowler to describe the dynamics of dunes and we develop a numerical procedure based on splitting methods to approximate its solutions we begin by proving the convergence of the well known lie formula which is an approximation of the exact solution of order one in time we next use the split step fourier method to approximate the continuous problem using the fast fourier transform and the finite difference method our numerical experiments confirm the theoretical results

numerical method for volterra equation with a power type nonlinearity abstract in this work we prove that a family of explicit numerical methods is convergent when applied to a nonlinear volterra equation with a power type nonlinearity in that case the kernel is not of lipschitz type therefore the classical analysis cannot be utilized we indicate several difficulties that arise in the proofs and show how they can be remedied the tools that we use consist of variations on discreet gronwall s lemmas and comparison theorems additionally we give an upper bound on the convergence order we conclude the paper with a construction of a convergent method and apply it for solving some examples

henry gronwall type retarded integral inequalities and their applications to fractional differential equations with delay abstract this paper presents retarded integral inequalities of henry gronwall type applying these inequalities we study certain properties of solutions to fractional differential equations with delay

a smoothed particle hydrodynamics model for laser beam melting of ni based alloy 718 laser beam melting lbm also referred to as selective laser melting slm is an additive manufacturing am technology and pertains to the powder bed fusion pbf processes within this work a numerical simulation model of the lbm process based on the meshless computational method smoothed particle hydrodynamics sph in a multi phase and weakly compressible formulation is presented its implementation utilizes the parallelization capabilities of graphics processing units gpu for achieving a reduced computation time physical phenomena such as thermal conduction melting and re solidification convection and effects related to surface tension such as thermocapillarity are considered furthermore the influence of the recoil pressure induced by evaporating atoms from the melt pool surface is taken into account the material properties of relevance e g dynamic viscosity thermal conductivity and absorptivity for the investigated alloy inconel 718 respectively alloy 718 are modeled by means of temperature dependent functions the underlying material data originate from literature the simulation results are compared with experimental findings for single melt tracks to evaluate the model validity with regard to the process parameters scanning velocity and laser power

a generalized gronwall inequality and its application to a fractional differential equation this paper presents a generalized gronwall inequality with singularity using the inequality we study the dependence of the solution on the order and the initial condition of a fractional differential equation

approximate controllability of fractional evolution systems with riemann liouville fractional derivatives in this paper we deal with the control systems governed by fractional evolution differential equations involving riemann liouville fractional derivatives in banach spaces our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions under these conditions the approximate controllability of the associated fractional evolution systems involving riemann liouville fractional derivatives is formulated and proved

existence and asymptotic behavior for a convection problem abstract we prove global existence and exponential decay of solutions for a system which arise in thermal convection flow for sufficiently small initial data these results improve previous ones in funkcial ekvac 34 1991 449 further we investigate the behavior of solutions for arbitrarily large initial data in particular we show that the length of the interval on which we have existence and exponential decay is inverse proportional to the size of the initial data

convergence and stability of compact finite difference method for nonlinear time fractional reaction diffusion equations with delay abstract this paper is concerned with numerical solutions of nonlinear time fractional reaction diffusion equations with time delay a linearized compact finite difference scheme is proposed to solve the equations in terms of a new developed fractional gronwall type inequality convergence and stability of the proposed scheme are obtained numerical experiments are given to illustrate the theoretical results

stability and pinning synchronization analysis of fractional order delayed cohen grossberg neural networks with discontinuous activations abstract this article we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed cohen grossberg neural networks with discontinuous neuron activation functions fcgnndds first under the framework of filippov theory and differential inclusion theoretical analysis the global existence of filippov solution for fcgnndds is studied by means of the given growth condition second by virtue of suitable lyapunov functional young inequality and comparison theorem for fractional order delayed linear system some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations third the global asymptotic synchronization condition for fcgnndds is obtained based on the pinning control at last two numerical simulations are given to verify the theoretical findings

a pairwise relaxing incompressible smoothed particle hydrodynamics scheme abstract we present a formulation of incompressible smoothed particle hydrodynamics isph method that utilizes pairwise relaxing kernel to achieve approximately first order consistency previous high order formulations by using reproduced and corrected kernel function have had difficulties in ensuring momentum conservation in the new scheme relaxing constants for each kernel function are determined pair wisely throughout the entire calculation domain by enforcing the taylor series consistency condition we call this modified isph method pairwise relaxing isph or pr isph pr isph retains high order accuracy for non uniform particle distributions the spatial symmetry of the kernel function is kept in pr isph thus momentum is strictly conserved several two dimensional benchmark calculations are conducted to demonstrate the accuracy as well as the conservation property of the pr isph

existence results for fractional order semilinear functional differential equations with nondense domain abstract in this paper we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the riemann liouville derivative our approach is based on integrated semigroup theory the banach contraction principle and the nonlinear alternative of leray schauder type

an lq lp theory for the time fractional evolution equations with variable coefficients abstract we introduce an l q l p theory for the semilinear fractional equations of the type 0 1 t u t x a i j t x u x i x j t x f t x u t 0 x r d here 0 2 p q 1 and t is the caupto fractional derivative of order uniqueness existence and l q l p estimates of solutions are obtained the leading coefficients a i j t x are assumed to be piecewise continuous in t and uniformly continuous in x in particular a i j t x are allowed to be discontinuous with respect to the time variable our approach is based on classical tools in pde theories such as the marcinkiewicz interpolation theorem the calderon zygmund theorem and perturbation arguments

sph simulations of time dependent poiseuille flow at low reynolds numbers a working smoothed particle hydrodynamics sph formalism for solving the equations of motion of a viscous fluid is presented the method is based on a standard symmetrized sph expression for the viscous forces which involves only first order derivatives of the kernel through a direct evaluation of the viscous stress tensor therefore the interpolation can be performed using low order kernels of compact support without compromising the accuracy and stability of the results in principle the scheme is suitable for treating compressible fluids with arbitrary shear and bulk viscosities here we demonstrate that when it is combined with the pressure gradient correction proposed by morris et al the method is also suitable for solving the navier stokes equations for incompressible flows without any further assumptions simulations using the method show close agreement with the analytic series solutions for plane poiseuille and hagen poiseuille flows at very low reynolds numbers at least for these specific tests the results obtained are essentially independent of employing either a cubic or a quintic spline kernel

weakly singular gronwall inequalities and applications to fractional differential equations abstract we obtain some new gronwall type inequalities which are applicable to some weakly singular volterra integral equations similar to the ones first studied by d henry the main interest is that we consider cases with a double singularity and we obtain explicit l bounds rather than l 1 bounds furthermore our bounds involve the exponential function and not the mittag leffler function as in some previous works we give applications to some volterra integral equations with a doubly singular kernel that arise from caputo fractional differential equations where as opposed to previous papers we have a singularity in the nonlinearity

on some new inequalities related to certain inequalities in the theory of differential equations in the present paper we establish some new integral inequalities related to a certain inequality arising in the theory of differential equations the discrete analogues of the main results are also given the analysis used in the proofs is elementary and the results established here provide new estimates for these types of inequalities

a lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue we present a novel lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue linear solids are represented by the lagrangian formulation of the stress strain relationship that is extended to nonlinear solids by using the lagrangian evolution of the deformation gradient described in a moving framework the present method introduces a level set description along with the particles to capture the body deformations and to enforce the boundary conditions furthermore the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure the method is validated in several benchmark problems in two and three dimensions and the results compare well with the results of respective finite elements simulations in simulations of large solid deformation under plane strain compression the finite element solver exhibits spurious structures that are not present in the lagrangian particle simulations the particle simulations are compared with experimental results in an aspiration test of liver tissue

modified gronwall s inequality and its application to stabilization problem for semilinear parabolic systems abstract this paper deals with the stabilization of semilinear parabolic distributed systems by means of boundary controls the partial differential equation describing the system is formulated as a semilinear evolution equation in a hilbert space by using a variable transformation here it is shown that the solution globally exists for the closed loop system which installs a finite dimensional dynamic compensator by using the properties of an analytic semigroup moreover a sufficient condition for stabilization of the system is derived by making use of the modified gronwall s inequality developed in this paper

explicit bounds on some new nonlinear integral inequalities with delay the purpose of the present note is to establish some new delay integral inequalities which provide explicit bounds on unknown functions and generalize some results of li et al some new delay integral inequalities and their applications j comput appl math 180 2005 191 200 the inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations

generalization of a retarded gronwall like inequality and its applications abstract this paper generalizes a lipovan s result of gronwall like inequalities j math anal appl 252 2000 389 to a new type of retarded inequalities which includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals from our result bihari s result and pinto s result can be deduced as some special cases our result can be applied to give the global existence and estimate solutions we also apply it to improve an estimation for almost periodicity of an invariant manifold

constrained exact controllability of semilinear systems in the paper infinite dimensional dynamical control systems described by semilinear abstract differential equations are considered using a generalized open mapping theorem sufficient conditions for constrained exact local controllability are formulated and proved it is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero constrained exact local controllability of semilinear abstract second order dynamical systems are also formulated and proved as an illustrative example constrained exact local controllability problem for semilinear hyperbolic type distributed parameters dynamical system is solved in details some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented

optimal control of feedback control systems governed by hemivariational inequalities this paper is mainly concerned with the feedback control systems governed by evolution hemivariational inequalities by using the properties of multimaps and clarke s subdifferential we formulate some sufficient conditions to guarantee the existence result of feasible pairs of the feedback control systems we also present an existence result of optimal control pairs for an optimal control problem we emphasize that our results cannot be obtained straightforwardly from the previous works

some new generalized gronwall bellman type discrete fractional inequalities some new gronwall bellman type discrete fractional inequalities are established explicit bounds for unknown functions in fractional inequalities are derived properties of solutions of one certain fractional difference equation are researched in this paper we present some new generalized gronwall bellman type discrete fractional inequalities including fractional sum inequalities and fractional difference inequalities these inequalities are of new forms compared with the existing results so far in the literature and can be used to provide explicit bounds for unknown functions concerned for illustrating the effectiveness of the presented results we apply them to research qualitative and quantitative properties for the solutions of an ivp with respect to a fractional difference equation

on some generalized retarded integral inequalities and the qualitative analysis of integral equations abstract in this paper we obtain estimates on solutions of some retarded integral inequalities which include retarded gronwall like inequalities and retarded volterra fredholm type inequalities some particular cases with weakly singular kernels are discussed we also apply our results to investigate the boundedness uniqueness and continuous dependence of solutions of some integral equations

on the oscillatory behavior of solutions of nonlinear fractional differential equations the study of oscillation theory for fractional differential equations has been initiated by grace et al 14 in this paper we establish some new criteria for the oscillation of fractional differential equations with the caputo derivative of the form c d a x t e t f t x t a 1 1 2 we also present the conditions under which all solutions of this equation are asymptotic to at b as t for some real numbers a b we shall employ a different technique rather than that in 14

a new approach to an analysis of henry type integral inequalities and their bihari type versions abstract in this paper we propose a new method to solve integral inequalities of henry gronwall type and their bihari nonlinear version nonlinear integral inequalities with weakly singular kernels and with multiple integrals as well as a modification of the ou iang pachpatte inequality are also treated

neutral fuzzy fractional functional differential equations abstract in this paper a class of fuzzy fractional functional differential equations of neutral type is investigated the existence uniqueness and iterative formula in the case of linear equations are obtained meanwhile the continuous dependence of solutions on initial data parameters and functions involved in right hand side of equation is also discussed several examples are given to illustrate the applications of our results

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

nonexistence of periodic solutions and s asymptotically periodic solutions in fractional difference equations nonexistence of periodic solution is proved for periodic right hand side existence of s asymptotically periodic solutions is discussed existence and uniqueness results are obtained for s asymptotically periodic solution nontrivial estimations of a ratio of gamma functions are used in this paper it is shown that a fractional difference equation with a periodic right hand side can not possess a periodic solution but it can have an s asymptotically periodic solution sufficient conditions are proved for the existence of a unique s asymptotically periodic solution an example is also given illustrating the obtained results

finite dimensional compensators for parabolic distributed systems with unbounded control and observation it is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback finite dimensional means here that the dynamics relating the input to the output is finite dimensional a constructive design algorithm is presented and several examples are considered

an incompressible multi phase sph method an incompressible multi phase sph method is proposed in this method a fractional time step method is introduced to enforce both the zero density variation condition and the velocity divergence free condition at each full time step to obtain sharp density and viscosity discontinuities in an incompressible multi phase flow a new multi phase projection formulation in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed numerical examples for taylor green flow capillary waves drop deformation in shear flows and for rayleigh taylor instability are presented and compared to theoretical solutions or references from literature the results suggest good accuracy and convergence properties of the proposed method

feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations general second order parabolic and hyperbolic equations on a bounded domain are considered the input is applied in the neumann or mixed boundary condition and is expressed as a finite dimensional feedback in the parabolic case the feedback acts in particular on the dirichlet trace of the solution here it is shown that the resulting closed loop system defines a feedback c0 semigroup on l2 in fact on h32 2 0 that is both analytic and compact for positive times and whose generator has compact resolvent in the hyperbolic case the feedback acts on the position vector only or on its dirichlet trace in a special case here a similar result is established regarding the existence of a feedback c0 cosine operator moreover an example is given which hints that the class of prescribed feedbacks acting on the dirichlet trace cannot be substantially enlarged functional analytic techniques are employed in particular perturbation theory however perturbation theory for the original variable fails on l2 the space in which the final result is sought therefore our approach employs perturbation theory after a suitable continuous extension on the larger space h12 2

qualitative analysis for solutions of a certain more generalized two dimensional fractional differential system with hadamard derivative based on an elementary inequality and two gronwall bellman type integral inequality systems this paper generalizes the results for the constructions of explicit bounds and the qualitative properties for the solutions of certain fractional systems with hadamard derivative established in a recent paper by the authors the major generalizations come from linearization method and de singular approach after overcoming some difficulties in the hadamard type singular kernel

finite time stability of neutral fractional order time delay systems with lipschitz nonlinearities abstract this paper is concerned with finite time stability of neutral fractional order time delay systems with lipschitz nonlinearities by use of the method of steps and the generalized gronwall inequality a new criterion on finite time stability is obtained two numerical examples are given to illustrate the effectiveness of our main results

approximate controllability for fractional semilinear parabolic equations abstract in this paper we deal with the control systems described by a large class of fractional semilinear parabolic equations firstly we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate banach space secondly we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator nonlinear analysis method and fixed point theorem then the approximate controllability of the fractional semilinear parabolic equations is formulated and proved at the end of the paper an example is given to illustrate our main results

finite difference methods with non uniform meshes for nonlinear fractional differential equations in this article finite difference methods with non uniform meshes for solving nonlinear fractional differential equations are presented where the non equidistant stepsize is non decreasing the rectangle formula and trapezoid formula are proposed based on the non uniform meshes combining the above two methods we then establish the predictor corrector scheme the error and stability analysis are carefully investigated at last numerical examples are carried out to verify the theoretical analysis besides the comparisons between non uniform and uniform meshes are given where the non uniform meshes show the better performance when dealing with the less smooth problems

stabilization and structural assignment of dirichlet boundary feedback parabolic equations a parabolic equation defined on a bounded domain is considered with input acting on the boundary through the dirichlet b c expressed as a specified finite dimensional feedback of the solution the free system zero b c is assumed throughout to be unstable two main results are established first we provide in 2 a novel proof that fully solves the corresponding boundary feedback stabilization problem thereby removing an annoying assumption required by the technique of appl math optim 6 1980 pp 201 220 under certain natural algebraic conditions based on the finitely many unstable eigenvalues we establish the existence of general boundary vectors for which the corresponding feedback semigroup decays exponentially to zero in the l 2 omega operator norm or more generally in the h s omega operator norm 0 leqq s frac 1 2 however most of the paper is devoted to the second problem structural or spectral assignment which is a natural question relevant to the selfadj

some nonlinear gronwall bellman type retarded integral inequalities with power and their applications abstract the purpose of this paper is to establish some new retarded integral inequalities of gronwall bellman type which generalizes some known integral inequalities we use two lemmas to simplify the complex inequalities and give an upper bound estimation of the unknown function the inequalities given here can be used in the analysis of the qualitative properties of certain classes of differential equations and integral equations we apply our results to the boundedness of the solutions of integral equations and differential system

stability analysis of fractional order memristive discontinuous neural networks with partial state control abstract this paper investigates exponential stability of fractional order memristive discontinuous neural networks fmdnns under the framework of the fractional order filippov solution and differential inclusion theory the global existence of the solution for the fmdnns is studied by a given growth conditions based on fractional stability theoryand the properties of the mittag leffler function some new criteria for the stability of fmdnns are obtained by using effective partial state impulsive control which only needs to control a small fraction of the states at every impulsive moment these states of the trajectory far away from the desired trajectory will be firstly controlled the relations between stable region and fractional order control parameters and control rate are discussed finally a numerical simulation is given to verify the effectiveness of the theoretical analysis

exponents of indecomposability abstract let r n be integers n h r a such that am is r indecomposable for all m h r a the integer h r a is called the strict exponent of r indecomposability of the primitive matrix a it refines the well known exponent exp a h n 1 a brualdi and liu czechoslovak math j 40 115 1990 659 670 proc amer math soc 112 4 1991 1193 1201 conjectured that h o a n 2 4 and h l a n 1 2 4 we show that h r a max 1 s n s r 1 1 where s is the smallest positive integer such that trace as 0 this improves the conjectured bounds for h o and h l

nonlinear impulsive problems for fractional differential equations and ulam stability in this paper the first purpose is treating cauchy problems and boundary value problems for nonlinear impulsive differential equations with caputo fractional derivative we introduce the concept of piecewise continuous solutions for impulsive cauchy problems and impulsive boundary value problems respectively by using a new fixed point theorem we obtain many new existence uniqueness and data dependence results of solutions via some generalized singular gronwall inequalities the second purpose is discussing ulam stability for impulsive fractional differential equations some new concepts in stability of impulsive fractional differential equations are offered from different perspectives some applications of our results are also provided

a class of nonlinear non instantaneous impulsive differential equations involving parameters and fractional order abstract in this article we study asymptotic and smooth properties of solutions to nonlinear non instantaneous impulsive differential equations involving parameters of integer order and fractional order we introduce the concept of continuous dependence and differentiability of solutions and establish sufficient conditions to guarantee the solution depends continuously and is differentiable on the initial condition impulsive parameters and junction parameters finally two models of non instantaneous impulsive logistic equations are given to illustrate our results

integral inequalities of systems and the estimate for solutions of certain nonlinear two dimensional fractional differential systems this paper generalizes the results for the constructions of explicit bounds and the qualitative properties for the solutions of certain two dimensional fractional differential systems established in a recent paper of the authors the main generalizations come from an elementary inequality and by means of the modification of medved s de singular approach

gronwall bellman and pachpatte type integral inequalities with applications abstract in this article a number of two dimensional nonlinear retarded integral inequalities of gronwall bellman type which can be used as ready and powerful tools in the analysis of various classes of partial differential integral and integro differential equations are presented applications of nonlinear retarded integral inequalities are also presented

a retarded gronwall like inequality and its applications we prove a gronwall like inequality and present some of its applications to the qualitative study of retarded differential equations the problems of global continuation of the solutions and the existence of nonoscillatory solutions are considered by means of examples we show the usefulness of our results

a survey on the initial value problems of fuzzy implicit fractional differential equations abstract the purpose of this paper is to present some basic theories of various classes of initial value problems of implicit fractional differential equation involving the caputo fuzzy type riemann liouville fuzzy type and hadamard fuzzy type concepts of fractional derivative in the case of the order 0 1 in particular the existence and uniqueness results of solution for the given initial value problems of implicit fractional differential equations is investigated in addition some results concerning continuous dependence of solutions on perturbations of the given parameters namely of the initial conditions of the function and parameters on the right hand side of the order of fractional derivative are analyzed finally some examples are given to illustrate our main results

some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations abstract some new weakly singular integral inequalities of gronwall bellman type are established which generalized some known weakly singular inequalities and can be used in the analysis of various problems in the theory of certain classes of differential equations integral equations and evolution equations some applications to fractional differential and integral equations are also indicated

on some qualitative properties for solutions of a certain two dimensional fractional differential systems abstract by means of the modification of medve s de singular method and a result of two dimensional linear integral inequalities components wise not on some norm upper bounds are obtained for solutions of a class of nonlinear two dimensional systems of fractional differential equations the uniqueness and continuous dependence of the solutions are also discussed here

exploring delayed mittag leffler type matrix functions to study finite time stability of fractional delay differential equations abstract in this paper we introduce a concept of delayed two parameters mittag leffler type matrix function which is an extension of the classical mittag leffler matrix function with the help of the delayed two parameters mittag leffler type matrix function we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method in addition we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations thereafter we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term finally an example is presented to illustrate the validity of the main theorems

an inverse time dependent source problem for a time space fractional diffusion equation abstract this paper is devoted to identify a time dependent source term in a time space fractional diffusion equation by using the usual initial and boundary data and an additional measurement data at an inner point the existence and uniqueness of a weak solution for the corresponding direct problem with homogeneous dirichlet boundary condition are proved we provide the uniqueness and a stability estimate for the inverse time dependent source problem based on the separation of variables we transform the inverse source problem into a first kind volterra integral equation with the source term as the unknown function and then show the ill posedness of the problem further we use a boundary element method combined with a generalized tikhonov regularization to solve the volterra integral equation of the fist kind the generalized cross validation rule for the choice of regularization parameter is applied to obtain a stable numerical approximation to the time dependent source term numerical experiments for six examples in one dimensional and two dimensional cases show that our proposed method is effective and stable

instability of smoothed particle hydrodynamics applied to poiseuille flows abstract smoothed particle hydrodynamics sph has been widely applied to flows with free surface multi phase flow and systems with complex boundary geometry however it has been shown that sph suffers from transverse instability when applied to simple wall bounded shear flows such as poiseuille and couette flows at moderate and high reynolds number re 1 casting the application of sph to practical situations into doubt where the reynolds number is frequently large here we consider poiseuille flows for a wide range of reynolds number and find that the documented instability of sph can be avoided by using appropriate ratio of smoothing length to particle spacing in combination with a density re initialization technique which has not been systematically investigated in simulations of simple shear flows we also probe the source of the instability and point out the limitations of sph for wall bounded shear flows at high reynolds number

several integral inequalities and their applications in nonlinear differential systems in this paper several new integral inequalities are presented which are effective in dealing with the integro differential inequalities whose variable exponents are greater than one compared with existing integral inequalities those proposed here can be applied to more complicated differential equations the notions of uniform lipschitz stability are generalized and the relations between these notions are analyzed several sufficient conditions about uniform lipschitz asymptotic stability of nonlinear systems are established by the proposed integral inequalities these sufficiently conditions can be similarly generalized to linearly perturbed differential systems that appear in the literature finally an example of uniform lipschitz asymptotic stability of nonlinear differential systems is shown

estimation of unknown function of a class of integral inequalities and applications in fractional integral equations in this paper we establish a class of iterated integral inequalities which includes a nonconstant term outside the integrals the upper bound of the embedded unknown function is estimated explicitly by adopting novel analysis techniques such as change of variable amplification method differential and integration the derived result can be applied in the study of qualitative properties of solutions of fractional integral equations

a positioning algorithm for sph ghost particles in smoothly curved geometries abstract an algorithm to place ghost particles across the domain boundary in the context of smoothed particle hydrodynamics sph is derived from basic principles and constructed for several simple three dimensional geometries the performance of the algorithm is compared against the more commonly used mirrored with respect to the local tangent plane approach and shown to converge to it whenever the distance of the particles to the reflecting boundary is much smaller than a local measure of the surface s curvature the algorithm is demonstrated tested and compared against the usual approach via simulations of a compressible flow around a cylinder and the numerical cost of implementing it is addressed we conclude that use of ghost particles to enforce boundary conditions is not only viable in the presence of smoothly curved boundaries but more robust than the usual method for low resolution scenarios

integral inequalities and global solutions of semilinear evolution equations a criterion for the nonexplosion of solutions to semilinear evolution equations on banach spaces is proved the result is obtained by applying a modification of the bihari type inequality to the case of a weakly singular nonlinear integral inequality

power type estimates for a nonlinear fractional differential equation abstract in this work we are concerned with a family of nonlinear ordinary differential equations of fractional order it is proved that solutions of these equations with weighted initial data exist globally and decay as a power function

a generalized wall boundary condition for smoothed particle hydrodynamics in this paper we present a new formulation of the boundary condition at static and moving solid walls in sph simulations our general approach is both applicable to two and three dimensions and is very simple compared to previous wall boundary formulations based on a local force balance between wall and fluid particles we apply a pressure boundary condition on the solid particles to prevent wall penetration this method can handle sharp corners and complex geometries as is demonstrated with several examples a validation shows that we recover hydrostatic equilibrium conditions in a static tank and a comparison of the classical dam break simulation with state of the art results in literature shows good agreement we simulate various problems such as the flow around a cylinder and the backward facing step at re 100 to demonstrate the general applicability of this new method

on the concept of general solution for impulsive differential equations of fractional order q 0 1 in this paper for impulsive differential equations with fractional order q 0 1 we show that the formula of solutions in cited papers are incorrect secondly we find out a formula of the general solution for impulsive cauchy problem with caputo fractional derivative q 0 1 further for a kind of impulsive fractional differential equations system with special initial value we come to an existence result for it by applying fixed point methods

the base sets of primitive zero symmetric sign pattern matrices abstract in j y shao l h you bound on the base of irreducible generalized sign pattern matrices discrete math in press shao and you extended the concept of the base from powerful sign pattern matrices to non powerful and generalized sign pattern matrices in this paper we study the bases of primitive zero symmetric sign pattern and generalized sign pattern matrices sharp upper bounds of the bases are obtained we also show that there exist no gaps in the base sets of the classes of such matrices

analytic study on linear neutral fractional differential equations this paper is devoted to investigating linear neutral fractional differential equations with constant coefficients the existence uniqueness and iterative formula of the solution are obtained meanwhile dependence of the solution on initial value and the general solution represented by a fundamental solution matrix are discussed several examples are given to illustrate the applications of our results some conclusions in the literature are extended greatly

new criteria on finite time stability of fractional order hopfield neural networks with time delays in this article the finite time stability fts of fractional order hopfield neural networks with time delays fhnntds is studied a widely used inequality in investigating the stability of the fractional order neural networks is fractional order gronwall inequality related to the mittag leffler function which cannot be directly used to study the stability of the factional order neural networks with time delays in the existing works related to fractional order gronwall inequality with time delays the order 0 was divided into two cases 0 0 5 and 0 5 in this article a new fractional order gronwall integral inequality with time delay and the unified form for all the fractional order 0 is developed which can be widely applied to investigate fts of various fractional order systems with time delays based on this new inequality a new criterion for the fts of fhnntds is derived compared with the existing criteria in which fractional order 0 1 was divided into two cases 0 0 5 and 0 5 1 the obtained results in this article are presented in the unified form of fractional order 0 1 and convenient to verify more importantly the criteria in this article are less conservative than some existing ones finally two numerical examples are given to demonstrate the validity of the proposed results

existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay we deal in this paper with the mild solution for fractional semilinear differential equations with infinite delay d ax t ax t f t x t bx t email protected 0 t x t email protected t email protected 0 with t 0 and 0 0 on a complex banach space x by means of classical fixed points methods

tau approximation method for the weakly singular volterra hammerstein integral equations in this paper we propose a useful method based on the tau method with arbitrary bases to find the numerical solution of weakly singular voletrra hammerstein integral equations in this scheme an operational approach using the orthogonal polynomial bases is presented for converting the problem under consideration to its matrix vector representation error analysis of this method is also presented some numerical examples are provided to illustrate the accuracy and computational efficiency of the method

fractional integral inequalities and applications fractional integral inequality results when 0 q 1 are developed when the nonlinear term is increasing in u and satisfies a one sided lipschitz condition using the integral inequality result and the computation of the solution of the linear fractional equation of variable coefficients gronwall inequality results are established this yields the results of q 1 as a special case as an application of this the uniqueness and continuous dependence of the solution on the initial parameters of the nonlinear fractional differential equations are established

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

explicit solutions of fractional integral and differential equations involving erdelyi kober operators by means of fractional calculus techniques we find explicit solutions of volterra integral equations of second kind and fractional differential equations involving erdelyi kober fractional integrals or derivatives we use the transmutation method to reduce the solutions of these equations to known solutions of simpler riemann liouville equations of the same type some examples are given

a new approach for solving integro differential equations of variable order abstract in this work we consider a class of nonlinear integro differential equations of variable order existence uniqueness and stability results are discussed for solving the considered equations operational matrices based on the shifted legendre polynomials are used first we approximate the unknown function and its derivatives in terms of the shifted legendre polynomials then by substituting these approximations into the equation and using the properties of the shifted legendre polynomials together with the collocation points the main problem is reduced to a system of nonlinear algebraic equations an error bound is proved for the approximate solution obtained by the proposed method finally some illustrative examples are included to show the efficiency and accuracy of the proposed scheme