razumikhin type theorems on general decay stability of stochastic functional differential equations with infinite delay to the best of the authors knowledge there are no results based on the so called razumikhin technique via a general decay stability for any type of stochastic differential equations in the present paper the razumikhin approach is applied to the study of both pth moment and almost sure stability on a general decay for stochastic functional differential equations with infinite delay the obtained results are extended to stochastic differential equations with infinite delay and distributed infinite delay some comments on how the considered approach could be extended to stochastic functional differential equations with finite delay are also given an example is presented to illustrate the usefulness of the theory

fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

automatic differentiation of characterizing sequences abstract gradient and hessian matrix of a real function of several variables play an important role in many numerical methods especially in nonlinear optimization but little effort has been devoted to the computation of these entities so far the hessian is not available this statement used to be an axiom in the optimization folklore for decades nevertheless we will show how to obtain gradient and hessian matrix of an explicitly given function automatically in an easy and straightforward manner no quotients of differences are used no manipulation of symbols is involved we deal with numbers not with formulas furthermore we show how to apply automatic differentiation in special situations arising in nonlinear optimization and in the multivariate halley method

fractional laplacian time space models for linear and nonlinear lossy media exhibiting arbitrary frequency power law dependency frequency dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2 the standard time domain partial differential equation models can describe merely two extreme cases of frequency independent and frequency squared dependent attenuations the otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation in this study a linear integro differential equation wave model was developed for the anomalous attenuation by using the space fractional laplacian operation and the strategy is then extended to the nonlinear burgers equation a new definition of the fractional laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional laplacian under the szabo s smallness approximation where attenuation is assumed to be much smaller than the wave number the linear model is found consistent with arbitrary frequency power law dependency

on the asymptotic behavior for neutral stochastic differential delay equations this note investigates the existence and uniqueness as well as the stability of the general decay rate of the global solution for neutral stochastic differential equations with time varying delay under a locally lipschitz condition a contractive condition and a monotonicity condition the stability results are derived by using the lyapunov function approach and some stochastic analysis techniques which not only cover the exponential stability in the p th p 0 moment and the almost sure exponential stability but also the polynomial stability in the p th p 0 moment and the almost sure polynomial stability two examples including one coupled system consisting of a mass spring damper connected to a pendulum and the nonlinear external random force are given to illustrate the effectiveness of the obtained results

ito type stochastic fuzzy differential equations with delay abstract in the paper we give some foundations for the studies of stochastic fuzzy delayed differential equations we prove the existence and uniqueness of solutions to such the equations to obtain our result we assume that the coefficients of the equation satisfy the lipschitz condition together with linear growth condition we estimate the distance between approximate solution and exact solution also the stability of solution with respect to the initial history is shown an application of stochastic fuzzy delayed differential equations in the modeling of population growth is indicated

existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay this paper investigates the existence and uniqueness theorem of solutions to neutral stochastic differential equations with infinite delay short for insfdes at a space bc 0 r d under the uniform lipschitz condition linear growth condition is weaken to obtain the moment estimate of the solution for insfdes furthermore the existence uniqueness theorem of the solution for insfdes is derived and the estimate for the error between approximate solution and exact solution is given on the other hand under the linear growth condition the uniform lipschitz condition is replaced by the local lipschitz condition the existence uniqueness theorem is also valid for insfdes on t 0 t moreover the existence uniqueness theorem still holds on interval t 0 where t 0 r is an arbitrary real number

exponential stability for stochastic neutral partial functional differential equations abstract in this paper we consider a class of stochastic neutral partial functional differential equations in a real separable hilbert space some conditions on the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths are obtained the known results in govindan t e govindan almost sure exponential stability for stochastic neutral partial functional differential equations stochastics 77 2005 139 154 liu and truman k liu a truman a note on almost sure exponential stability for stochastic partial functional differential equations statist probab lett 50 2000 273 278 and taniguchi t taniguchi almost sure exponential stability for stochastic partial functional differential equations stoch anal appl 16 1998 965 975 t taniguchi asymptotic stability theorems of semilinear stochastic evolution equations in hilbert spaces stochastics 53 1995 41 52 are generalized and improved

stability of highly nonlinear neutral stochastic differential delay equations abstract stability criteria for neutral stochastic differential delay equations nsddes have been studied intensively for the past several decades most of these criteria can only be applied to nsddes where their coefficients are either linear or nonlinear but bounded by linear functions this paper is concerned with the stability of hybrid nsddes without the linear growth condition to which we will refer as highly nonlinear ones the stability criteria established in this paper will be dependent on delays

on the approximations of solutions to neutral sdes with markovian switching and jumps under non lipschitz conditions abstract in this paper we investigate the existence and uniqueness of solutions to neutral stochastic differential equations with markovian switching and jumps nsdewmsjs under non lipschitz conditions on the other hand we present the euler approximate solutions for nsdewmsjs and show that the convergence of the euler approximate solutions to the true solutions by applying it o formula bihari s lemma and burkholder davis gundy s lemma some examples are provided to illustrate the main results

mean square stability of two classes of theta method for neutral stochastic differential delay equations in this paper a stochastic linear theta slt method is introduced and analyzed for neutral stochastic differential delay equations nsddes we give some conditions on neutral item drift and diffusion coefficients which admit that the diffusion coefficient can be highly nonlinear and does not necessarily satisfy a linear growth or global lipschitz condition it is proved that for all positive stepsizes the slt method with 1 2 1 is asymptotically mean stable and so is 0 1 2 under a stronger assumption furthermore we consider the split step theta sst method and obtain a similar but better result that is the sst method with 1 2 1 is exponentially mean stable and so is 0 1 2 finally two numerical examples are given to show the efficiency of the obtained results

razumikhin type theorems on p th moment exponential stability of impulsive stochastic delay differential equations this note develops razumikhin type theorems on pth moment exponential stability for general impulsive stochastic delay differential equations some applications are also given to some special types of impulsive stochastic delay differential equations two examples illustrate the effectiveness of the proposed results

some analytic approximations for neutral stochastic functional differential equations abstract we consider an analytic iterative method to approximate the solution of a neutral stochastic functional differential equation more precisely we define a sequence of approximate equations and we give sufficient conditions under which the approximate solutions converge with probability one and in p th moment sense p 2 to the solution of the initial equation we introduce the notion of the z algorithm for this iterative method and present some examples to illustrate the theory especially we point out that the well known picard method of iterations is a special z algorithm

stability in distribution of neutral stochastic functional differential equations with markovian switching abstract stability in distribution of stochastic differential equations with markovian switching and stochastic differential delay equations with markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems there are several papers which study this stability for stochastic differential equations with markovian switching and stochastic differential delay equations with markovian switching technically in our paper we are concerned with the general neutral stochastic functional differential equations with markovian switching and we derive the sufficient conditions for stability in distribution at the end of our paper one example is established to illustrate the theory of our work

fractal ladder models and power law wave equations extensive measurement of the ultrasonic attenuation coefficient in human and mammalian tissue has revealed a power law dependence on frequency to describe this power law behavior in tissue a hierarchical fractal network model is proposed the viscoelastic and self similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite ladder topology involving alternating springs and dashpots in the low frequency limit this ladder network yields a stress strain constitutive equation with a time fractional derivative by combining this constitutive equation with linearized conservation principles and an adiabatic equation of state the fractional partial differential equations previously proposed by m caputo linear models of dissipation whose q is almost frequency independent ii geophys j r astron soc 13 529 539 1967 and mg wismer finite element analysis of broadband acoustic pulses through inhomogeneous media with power law attenuation j acoust soc am 120 3493 3502 2006 are derived the resulting attenuation coefficient is a power law with exponents ranging between 1 and 2 while the phase velocity is in agreement with the kramers kronig relations the power law exponent is interpreted in terms of the mechanical structure and related to the spectral dimension of the underlying fractal geometry

approximations of solutions to neutral functional differential equations with nonlocal history conditions abstract this work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a hilbert space the approximation of solution to a class of such problems is studied moreover the convergence of faedo galerkin approximation of solution is shown for illustration an example is worked out

a k space method for coupled first order acoustic propagation equations a k space method for large scale simulation of ultrasonic pulse propagation is presented the present method which solves the coupled first order differential equations for wave propagation in inhomogeneous media is derived in a simple form analogous to previous finite difference methods with staggered spatial and temporal grids like k space methods based on second order wave equations the present method is exact for homogeneous media unconditionally stable for slow c r c0 media and highly accurate for general weakly scattering media in addition unlike previous k space methods the form of the method allows straightforward inclusion of relaxation absorption and perfectly matched layer pml nonreflecting boundary conditions numerical examples illustrate the capabilities of the present k space method for weakly inhomogeneous media accurate results are obtained using coarser temporal and spatial steps than possible with comparable finite difference and pseudospectral methods the low dispers

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay this paper establishes the existence and uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate this result may be used to examine almost sure robust stability to illustrate our idea more carefully we carefully discuss a scalar stochastic integro differential equation with neutral type and its asymptotic stability including the exponential stability and the polynomial stability

nonlinear differential equations with nonlocal conditions in banach spaces abstract in this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in banach spaces we derive conditions under which the integral solutions exist

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

the existence of solutions for impulsive neutral functional differential equations this work deals with the existence of mild solutions for a class of impulsive functional differential equations of the neutral type associated with the family of linear closed not necessarily bounded operators a t email protected i

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

exponential stability in mean square of neutral stochastic differential functional equations abstract the aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form d x t g xt f t x t g t xt dt t xt dw t where xt x t s s 0 with 0 is the past history of the solution several interesting examples are a given for illustration

delay dependent robust stability of uncertain neutral type it stochastic systems with markovian jumping parameters this paper investigates the problem of mean square exponential stability for uncertain neutral stochastic systems with time delays and markovian jumping parameters based on the new results on expectations of stochastic cross terms containing the it o integral by song et al 2013 a new lyapunov krasovskii function is established and then an improved mean square exponential stability criterion is derived the derived results extend the conclusions recently presented in song et al 2013 in fact the system discussed in song et al 2013 is a special case of ours finally two examples are provided to demonstrate the effectiveness of the proposed results

stability analysis of neutral stochastic differential delay equations driven by levy noises abstract this paper mainly analyzes the well posedness and the stability analysis for the global solution of neutral stochastic differential delay equations nsddes driven by levy noises by using an integral lemma and a lyapunov function approach the existence and uniqueness theorem is proved then by using the inequality technique and the stochastic analysis theory the exponential stability in pth p 2 moment of such equations is discussed by using another integral lemma and using the baralat lemma as well as the stochastic analysis the almost surely asymptotic stability is also studied finally one example is given to check the effectiveness of the findings derived

some new criteria on p th moment stability of stochastic functional differential equations with markovian switching this note gives some new razumikhin type theorems on th moment stability of stochastic functional differential equations with markovian switching sfdewms by using auxiliary ordinary differential equation the main results of this note allow the diffusion operator associated with the underlying sfdewms of the lyapunov function along a solution of the system to be not always negative an example is provided to illustrate the effectiveness of the proposed results

new criteria on exponential stability of neutral stochastic differential delay equations neutral stochastic differential delay equations nsddes have recently been studied intensively see e g v b kolmanovskii v r nosov stability and periodic modes of control systems with aftereffect nauka moscow 1981 x mao exponential stability in mean square of neutral stochastic differential functional equations systems control lett 26 1995 245 251 x mao razumikhin type theorems on exponential stability of neutral stochastic functional differential equations siam j math anal 28 2 1997 389 401 x mao stochastic differential equations and their applications horwood publishing chichester 1997 more recently mao asymptotic properties of neutral stochastic differential delay equations stochastics and stochastics rep 68 2000 273 295 provided with some useful criteria on the exponential stability for nsddes however the criteria there require not only the coefficients of the nsddes to obey the linear growth condition but also the time delay to be a constant one of our aims in this paper is to remove these two restrictive conditions moreover the key condition on the diffusion operator associated with the underlying nsdde will take a much more general form our new stability criteria not only cover many highly non linear nsddes with variable time delays but they can also be verified much more easily than the known criteria

neutral stochastic functional differential equations with additive perturbations the paper deals with the solution to the neutral stochastic functional differential equation whose coefficients depend on small perturbations by comparing it with the solution to the corresponding unperturbed equation of the equal type we give conditions under which these solutions are close in the 2m th mean on finite time intervals and on intervals whose length tends to infinity as small perturbations tend to zero

ms stability of the euler maruyama method for stochastic differential delay equations the aim of this paper is to investigate the stability of the euler maruyama method for the stochastic differential equations with time delay the definition of ms stability of numerical methods is established the condition of the mean square stability of analytical solution is obtained for a linear scalar system with multiplicative noise and the ms stability of the numerical scheme is proved

a generalized fractional order elastodynamic theory for non local attenuating media this study presents a generalized elastodynamic theory based on fractional order operators capable of modelling the propagation of elastic waves in non local attenuating solids and across complex

a note on exponential stability for impulsive neutral stochastic partial functional differential equations in this note the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique some sufficient conditions are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained result

razumikhin type theorems on the moment stability of the exact and numerical solutions for the stochastic pantograph differential equations abstract in this paper we establish two different th moment type stability criterions on the exact and numerical solutions of the stochastic pantograph differential equations one is established by the virtue of lyapunov method and the other is used by the continuous and discrete razumikhin technique by comparing the two stability criterions we can easily see that the conditions constructed by the razumikhin type technique are better than those constructed by the virtue of lyapunov method using the conditions constructed for the th moment type stability we study the stability of the euler maruyama method and the backward euler maruyama method respectively for a special class of the stochastic pantograph differential equations finally examples are given to illustrate the consistence with the theoretical results on the th moment type stability

numerical solutions of neutral stochastic functional differential equations this paper examines the numerical solutions of neutral stochastic functional differential equations nsfdes d x t u x t f x t dt g x t dw t t geq 0 the key contribution is to establish the strong mean square convergence theory of the euler maruyama approximate solution under the local lipschitz condition the linear growth condition and contractive mapping these conditions are generally imposed to guarantee the existence and uniqueness of the true solution so the numerical results given here are obtained under quite general conditions although the way of analysis borrows from x mao lms j comput math 6 2003 pp 141 161 to cope with u x t several new techniques have been developed

generalised theory on asymptotic stability and boundedness of stochastic functional differential equations asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations sfdes see e g appleby and reynolds 2008 appleby and rodkina 2009 basin and rodkina 2008 khasminskii 1980 mao 1995 mao 1997 mao 2007 rodkina and basin 2007 shu lam and xu 2009 yang gao lam and shi 2009 yuan and lygeros 2005 and yuan and lygeros 2006 in general the existing results on asymptotic stability and boundedness of sfdes require i the coefficients of the sfdes obey the local lipschitz condition and the linear growth condition ii the diffusion operator of the sfdes acting on a c 2 1 function be bounded by a polynomial with the same order as the c 2 1 function however there are many sfdes which do not obey the linear growth condition moreover for such highly nonlinear sfdes the diffusion operator acting on a c 2 1 function is generally bounded by a polynomial with a higher order than the c 2 1 function hence the existing criteria on stability and boundedness for sfdes are not applicable and we see the necessity to develop new criteria our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up bound for the diffusion operator may take a much more general form

existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators abstract this paper is mainly concerned with existence of mild solutions for a first order impulsive neutral integrodifferential inclusions with nonlocal initial conditions in norm we assume that the linear part generates an analytic semigroup and transform it into an integral inclusion by using a fixed point theorem for multi valued maps due to dhage a main existence theorem is established finally we present an example to illustrate this main theorem

nonlocal nonlinear differential equations with a measure of noncompactness in banach spaces abstract in this paper we give the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions under the assumptions of the hausdorff measure of noncompactness in separable and uniformly smooth banach spaces

razumikhin type exponential stability criteria of neutral stochastic functional differential equations the paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations by using the razumikhin type technique the main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with lyapunov functionals the analysis is based on paper x mao razumikhin type theorems on exponential stability of neutral stochastic functional differential equations siam j math anal 28 2 1997 389 401 referring to mean square and almost sure exponential stability

modeling power law absorption and dispersion in viscoelastic solids using a split field and the fractional laplacian the absorption of compressional and shear waves in many viscoelastic solids has been experimentally shown to follow a frequency power law it is now well established that this type of loss behavior can be modeled using fractional derivatives however previous fractional constitutive equations for viscoelastic media are based on temporal fractional derivatives these operators are non local in time which makes them difficult to compute in a memory efficient manner here a fractional kelvin voigt model is derived based on the fractional laplacian this is obtained by splitting the particle velocity into compressional and shear components using a dyadic wavenumber tensor this allows the temporal fractional derivatives in the kelvin voigt model to be replaced with spatial fractional derivatives using a lossless dispersion relation with the appropriate compressional or shear wave speed the model is discretized using the fourier collocation spectral method which allows the fractional operators to be efficiently computed the field splitting also allows the use of a k space corrected finite difference scheme for time integration to minimize numerical dispersion the absorption and dispersion behavior of the fractional laplacian model is analyzed for both high and low loss materials the accuracy and utility of the model is then demonstrated through several numerical experiments including the transmission of focused ultrasound waves through the skull

time domain wave equations for lossy media obeying a frequency power law for attenuation described by a slowly varying power law function of frequency 0 y classical lossy time domain wave equations exist only for the restricted cases where y 0 or y 2 for the frequently occurring practical situation in which attenuation is much smaller than the wave number a lossy dispersion characteristic is derived that has the desired attenuation general power law dependence in order to obtain the corresponding time domain lossy wave equation time domain loss operators similar in function to existing derivative operators are developed through the use of generalized functions three forms of lossy wave equations are found depending on whether y is an even or odd integer or a noninteger a time domain expression of causality analogous in function to the kramers kronig relations in the frequency domain is used to derive the causal wave equations final causal versions of the time domain wave equations are obtained even for the cases where y 1 which according to the paley wiener th

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

on the pth moment exponential stability criteria of neutral stochastic functional differential equations the paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the ito type this investigation can be very complicated even in many special cases by using usual methods based on lyapunov functionals in this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations

exponential mean square stability of the theta approximations for neutral stochastic differential delay equations in this paper a split step theta sst method is introduced and analyzed for neutral stochastic differential delay equations nsddes it is proved that the sst method with 0 1 2 can recover the exponential mean square stability of the exact solution with some restrictive conditions on stepsize and the drift coefficient but for 1 2 1 the sst can reproduce the exponential mean square stability unconditionally then based on the stability results of sst scheme we examine the exponential mean square stability of the stochastic linear theta slt approximation for nsddes and obtain the similar stability results to that of the sst method moreover for sufficiently small stepsize we show that the decay rate as measured by the lyapunov exponent can be reproduced arbitrarily accurately these results show that different values of theta will drastically affect the exponential mean square stability of the two classes of theta approximations for nsddes

on mean square stability of two step maruyama methods for nonlinear neutral stochastic delay differential equations the asymptotic mean square stability of two step maruyama methods is considered for nonlinear neutral stochastic differential equations with constant time delay nsddes under the one sided lipschitz condition and the linear growth condition it is proved that a family of implicit two step maruyama methods can preserve the stability of the analytic solution in mean square sense numerical results for both a nonlinear nsdde and a system show that the family of two step maruyama methods have better stability than previous two step maruyama methods

automatic computation of partial derivatives and rounding error estimates with applications to large scale systems of nonlinear equations abstract recently a new approach has been proposed to efficiently compute the accurate values of partial derivatives of a function or functions and simultaneously to estimate the rounding errors in the computed function values in this paper the use of the method in the solution of nonlinear equations is investigated the method makes use of the computational graph and when applied to the evaluation of a function traverses it from the top the function node down to the bottom the input variable nodes a remarkable analogy is observed between the partial derivatives and the shortest paths on the computational graph the top down traversing on the computational graph has the following advantages over the existing algorithms using the bottom up traversing 1 the gradient of a function can be computed within the same complexity as that of the evaluation of the function alone the complexity being independent of the number of input variables 2 a fairly sharp estimate of the rounding error in the function evaluation is obtained on the basis of which a computationally meaningful norm may be introduced in the space of residuals to afford a convergence criterion for an iterative method of solving the system of nonlinear equations as an example a system of nonlinear equations with 108 variables for a distillation tower of a chemical plant is numerically analyzed in detail it is shown that by the use of the proposed method we could satisfactorily resolve two main problems encountered in computing a numerical solution of the system of nonlinear equations i e how to compute the accurate jacobian matrix and when we should stop the iteration

modeling power law absorption and dispersion for acoustic propagation using the fractional laplacian the efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics previous wave equations which use time domain fractional operators require the storage of the complete pressure field at previous time steps such operators are convolution based this makes them unsuitable for many three dimensional problems of interest here a wave equation that utilizes two lossy derivative operators based on the fractional laplacian is derived these operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into fourier based pseudospectral and k space methods without the increase in memory required by their time domain fractional counterparts a framework for encoding the developed wave equation using three coupled first order constitutive equations is discussed and the model is demonstrated through several one two and three dimensional simulations

razumikhin type theorems on stability of neutral stochastic functional differential equations recently mao 1995 initiated the study of exponential stability of neutral stochastic functional differential equations nsfdes and employed the razumikhin techniques to investigated the stability problem of nsfdes however the importance of general asymptotic stability has not been considered this paper studies razumikhin type theorems on general pth moment asymptotic stability of nsfdes the theorems established in this paper work for some cases to which the existing results cannot be applied

stability analysis of neutral stochastic delay differential equations by a generalisation of banach s contraction principle abstractin this paper we consider a class of neutral stochastic differential systems with variable delays and give sufficient conditions to ensure that the zero solution is asymptotically stable in the mean square by means of a generalisation of banach s contraction principle these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions the results are shown to improve the previous globally stable results derived in the literature

successive approximation of neutral functional stochastic differential equations with variable delays by using successive approximation we prove the existence and uniqueness of initial value problem for stochastic differential equations driven by both the cylindrical brownian motion and by the variable delays in a hilbert space with non lipschitzian coefficients moreover the numerical solutions are shown to converge uniformly to the analytical solutions of the stochastic differential equation

on some stability problems of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract this paper covers the topic of both the p th moment p 2 and almost sure stability of impulsive stochastic cohen grossberg neural networks with mixed time delays we partially use a known result on exponential stability of impulsive stochastic functional differential systems based on the razumikhin type technique and extend it to the case of stochastic neural networks using the lyapunov function method and a gronwall type inequality additionally we consider the stability with respect to a general decay function which includes exponential but also more general lower rate decay functions as the polynomial and the logarithmic ones this fact gives us the opportunity to study general decay almost sure stability even when the exponential one cannot be discussed suitable examples which support the theory are also presented

a causal and fractional all frequency wave equation for lossy media this work presents a lossy partial differential acoustic wave equation including fractional derivative terms it is derived from first principles of physics mass and momentum conservation and an equation of state given by the fractional zener stress strain constitutive relation for a derivative order in the fractional zener relation the resulting absorption k obeys frequency power laws as k 1 in a low frequency regime k 1 2 in an intermediate frequency regime and k 1 in a high frequency regime the value 1 corresponds to the case of a single relaxation process the wave equation is causal for all frequencies in addition the sound speed does not diverge as the frequency approaches infinity this is an improvement over a previously published wave equation building on the fractional kelvin voigt constitutive relation

simulation of fractionally damped mechanical systems by means of a newmark diffusive scheme a newmark diffusive scheme is presented for the time domain solution of dynamic systems containing fractional derivatives this scheme combines a classical newmark time integration method used to solve second order mechanical systems obtained for example after finite element discretization with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations which can be seen as internal memory variables the focus is given on the algorithm implementation into a finite element framework the strategies for choosing diffusive parameters and applications to beam structures with a fractional zener model

a k space green s function solution for acoustic initial value problems in homogeneous media with power law absorption an efficient green s function solution for acoustic initial value problems in homogeneous media with power law absorption is derived the solution is based on the homogeneous wave equation for lossless media with two additional terms these terms are dependent on the fractional laplacian and separately account for power law absorption and dispersion given initial conditions for the pressure and its temporal derivative the solution allows the pressure field for any time t 0 to be calculated in a single step using the fourier transform and an exact k space time propagator for regularly spaced cartesian grids the former can be computed efficiently using the fast fourier transform because no time stepping is required the solution facilitates the efficient computation of the pressure field in one two or three dimensions without stability constraints several computational aspects of the solution are discussed including the effect of using a truncated fourier series to represent discrete initial condit

on a general decay stability of stochastic cohen grossberg neural networks with time varying delays abstract to the best of our knowledge there are only few results on general decay stability applied to stochastic neural networks for stochastic cohen grossberg neural networks with time varying delays we study in the present paper both the pth moment p 2 and almost sure stability on a general decay rate and partly generalize and improve some known results referring to the exponential stability we also extend the usual notion on a general decay function which allows us to study both the pth moment and almost sure stability even if the exponential stability cannot be shown some examples are presented to support and illustrate the theory

new criteria on asymptotic behavior of neutral stochastic functional differential equations this paper investigates the asymptotic behavior of neutral stochastic functional differential equations nsfdes under both the local lipschitz condition and the one dependent on the diffusion operator and on a coercivity term which is more general than the classical growth condition some sufficient conditions for stability with general decay rate and boundedness of nsfdes are derived via the lyapunov analysis method and some stochastic analysis techniques our results not only cover a wide class of highly nonlinear nsfdes but they can also deal with general stability issues including the polynomial stability and the exponential stability finally an illustrative example is provided to show the effectiveness of our theoretical results

existence of solutions for neutral functional differential evolution equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii s fixed point theorem we study the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions the results we obtained are a generalization and continuation of the recent results on this issue in the end an example is given to show the application of our results

existence results of semilinear differential equations with nonlocal initial conditions in banach spaces abstract in this paper we establish the existence results for semilinear differential systems with nonlocal initial conditions in banach spaces the approaches used are fixed point theorems combined with convex power condensing operators the first result obtained will be applied to a class of semilinear parabolic equations

moment exponential stability and integrability of stochastic functional differential equations abstract the main objective of the paper is to present sufficient conditions ensuring the p th mean and almost sure exponential stability as well as the p th mean integrability of solutions to non linear stochastic functional differential equations and especially to stochastic differential equations with time varying lags some examples are given to illustrate the theoretical considerations

biot jkd model simulation of 1d transient poroelastic waves with fractional derivatives a time domain numerical modeling of biot poroelastic waves is presented the viscous dissipation occurring in the pores is described using the dynamic permeability model developed by johnson koplik dashen jkd some of the coefficients in the biot jkd model are proportional to the square root of the frequency in the time domain these coefficients introduce order 1 2 shifted fractional derivatives involving a convolution product based on a diffusive representation the convolution kernel is replaced by a finite number of memory variables that satisfy local in time ordinary differential equations thanks to the dispersion relation the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest a splitting strategy is then applied numerically the propagative part of biot jkd equations is discretized using a fourth order ader scheme on a cartesian grid whereas the diffusive part is solved exactly comparisons with analytical solutions show the efficiency and the accuracy of this approach

an asynchronous parallel newton method a parallel newton method is described for the minimization of a twice continuously differentiable uniformly convex functionf x the algorithm generates a sequence x j which converges superlinearly to the global minimizer off x

asymptotic stability of second order neutral stochastic differential equations in this paper we study the existence and asymptotic stability in pth moment of mild solutions to second order nonlinear neutral stochastic differential equations further this result is extended to establish stability criterion for stochastic equations with impulsive effects with the help of fixed point strategy stochastic analysis technique and semigroup theory a set of novel sufficient conditions are derived for achieving the required result finally an example is provided to illustrate the obtained result

stochastic functional differential equations with infinite delay abstract the stability and boundedness of the solution for stochastic functional differential equation with finite delay have been studied by several authors but there is almost no work on the stability of the solutions for stochastic functional differential equations with infinite delay the main aim of this paper is to close this gap we establish criteria of pth moment t bounded for neutral stochastic functional differential equations with infinite delay and exponentially stable criteria for stochastic functional differential equations with infinite delay and we also illustrate the result with an example

on almost automorphic mild solutions for fractional semilinear initial value problems abstract this paper investigates almost automorphic mild solutions of the fractional semilinear equation d x t a x t f t x t 0 1 considered in a banach space x where a is a linear operator of sectorial type 0 some sufficient conditions are given for the existence uniqueness and uniform stability of almost automorphic mild solutions to this semilinear equation

the if problem in automatic differentiation abstract we deal with a severe problem that arises in the automatic differentiation of functions many computer programs defining a function employ statements of the form if b x then s1 else s2 where b x is a boolean expression and s1 and s2 denote subprograms this often leads to a piecewise definition of the function under consideration automatic differentiation of the pieces may be hazardous for instance in cases where the underlying function is differentiable but one or the other piece is not in such cases available software often fails to produce correct results to resolve this perplexity we distinguish between a function and its representations in particular we introduce the notion derivative consistent automatic differentiation applied to a derivative consistent representation of a function yields correct results

automatic differentiation of the vector that solves a parametric linear system abstract we consider a parametric linear system a s x s b s where a s is a regular matrix b s is a vector and s is a p dimensional parameter this equation represents an implicit definition of a function x it is shown that automatic differentiation techniques can be used to compute derivatives of x for given parameter value s especially we aim at the jacobian matrix and the hessian tensor of x these quantities are of particular interest in sensitivity analysis and structural optimization

a first order k space model for elastic wave propagation in heterogeneous media a pseudospectral model of linear elastic wave propagation is described based on the first order stress velocity equations of elastodynamics k space adjustments to the spectral gradient calculations are derived from the dyadic green s function solution to the second order elastic wave equation and used to a ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size and b also allows larger time steps without loss of accuracy in heterogeneous media the formulation in k space allows the wavefield to be split easily into compressional and shear parts a perfectly matched layer pml absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield the staggered grid which is essential for accurate simulations is described along with other practical details of the implementation the model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems the efficiency of the model is by virtue of the reduced point per wavelength requirement the use of the fast fourier transform fft to calculate the gradients in k space and larger time steps made possible by the k space adjustments

on the exponential stability in mean square of neutral stochastic functional differential equations in 1 2 some efforts have been devoted to the investigation of exponential stability in mean square of neutral stochastic functional differential equations however the results derived there are either difficult to demonstrate in a straightforward way for practical situations or somewhat too restricted to be applied to general neutral stochastic functional differential equations for instance nonautonomous cases in this paper we shall establish some results which are more effective and relatively easy to verify to obtain the required stability

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative