on a fractional integral equation of periodic functions involving weyl riesz operator in banach algebras abstract in this paper we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving weyl riesz fractional integral operator under the mixed generalized lipschitz caratheodory and monotonicity conditions the fixed point theorems due to dhage are the main tool in carrying out our proofs

the constant variation formulae for singular fractional differential systems with delay abstract this paper considers the caputo singular fractional differential systems with delay and the riemann liouville singular fractional differential systems with delay a new function is defined by the d inverse matrix and function two fundamental solutions are given the constant variation formulae for singular fractional differential systems with delay are obtained

strong optimal solutions of interval linear programming abstract this paper considers optimal solutions of general interval linear programming problems the new concepts of optimal solutions are introduced in a unified framework some existed optimal solution concepts of interval linear program such as weak and strong optimal solutions are special cases in this framework necessary and sufficient conditions for checking optimality are developed also the features of the proposed methods are illustrated by some examples

solutions of fractional multi order integral and differential equations using a poisson type transform abstract we consider a wide class of integral and ordinary differential equations of fractional multi orders 1 1 1 2 1 m depending on arbitrary parameters i 0 i r i 1 m denoting the differentiation operators by d d i i and by l l i i the corresponding integrations operators right inverse to d we first observe that d and l can be considered as operators of the generalized fractional calculus respectively as generalized fractional derivatives and integrals a solution of the homogeneous ode of this kind d y z y z 0 0 is the recently introduced multi index mittag leffler function e 1 i i z we find a poisson type integral transformation p generalizing the classical poisson integral formula that maps the cosm function into the multi index mittag leffler function and also transforms the simpler differentiation and integration operators of integer order m 1 dm d dz m and lm the m fold integration into the operators d and l thus from the known solution of the volterra type integral equation with the m fold integration lm via p as a transformation transmutation operator we find the corresponding solution of the integral equation y z l z f z then a solution of the fractional multi order differential equation d y z y z f z comes out in an explicit form as a series of integrals involving fox s h functions for each particularly chosen r h s function f z such a solution can be evaluated as an h function special cases of the equations considered here lead to solutions in terms of the mittag leffler bessel struve lommel and hyper bessel functions and some other known generalized hypergeometric functions

eigenvalue and stability of singular differential delay systems the eigenvalue and the stability of singular differential systems with delay are considered firstly we investigate some properties of the eigenvalue then give the exact exponential estimation for the fundamental solution and finally discuss the necessary and sufficient condition of uniform asymptotic stability

analytical solution of the linear fractional system of commensurate order a useful representation of fractional order systems is the state space representation for the linear fractional systems of commensurate order the state space representation is defined as for regular integer state space representation with the state vector differentiated to a real order this paper presents a solution of the linear fractional order systems of commensurate order in the state space the solution is obtained using a technique based on functions of square matrices and the cayley hamilton theorem the technique developed for linear systems of integer order is extended to derive analytical solutions of linear fractional systems of commensurate order the basic ideas and the derived formulations of the technique are presented both homogeneous and inhomogeneous cases with usual input functions are solved the solution is calculated in the form of a linear combination of suitable fundamental functions the presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approach

strong and uniform mean stability of cosine and sine operator functions abstract it is first observed that a uniformly bounded cosine operator function c and the associated sine function s are totally non stable then using a zero one law for the abel limit of a closed linear operator we prove some results concerning strong mean stability and uniform mean stability of c among them are 1 c is strongly c 1 mean stable or c 2 mean stable or abel mean stable if and only if 0 a c a 2 c is uniformly c 2 mean stable if and only if s is uniformly c 1 mean stable if and only if 0 t s s d s o t t if and only if sup t 0 0 t s s d s if and only if c is uniformly abel mean stable if and only if s is uniformly abel mean stable if and only if 0 a

the general vector solutions of such linear coupled matrix fractional differential equations by using kronecker structures in this paper we demonstrate how kronecker products and vector operator can be combined beautifully to solve and fit the non homogenous linear matrix fractional differential equations and such coupled linear matrix fractional differential equations the way exists which transform the given coupled matrix fractional differential equations by using kronecker structures into forms for which solutions may be readily computed some important and interesting special cases of the general system of non homogeneous linear matrix fractional differential equations of fractional order are also considered which includes the non homogenous linear fractional dynamical system with delays in control finally a brief comparison between the fractional and integer order vector solutions and some examples are given to illustrate our new approaches

robust stability analysis of fractional order uncertain singular nonlinear system with external disturbance this paper investigates robust stability for fractional order fo singular nonlinear systems the fo system is disturbed by external uncertainty and disturbance a central analysis technique is enabled by proposing a fundamental boundedness lemma for the first time this lemma is used for robust stability analysis of fo systems especially for mittag leffler stability analysis of fo nonlinear systems more importantly how to obtain a more accurate bound is given to reduce conservative an fo proportional derivative pd controller is proposed to normalize the fo singular system furthermore a criterion for stability of the normalized fo nonlinear systems is provided by linear matrix inequalities lmis finally two illustrative simulation examples are presented to illustrate effectiveness of the proposed stability notion

on the existence and uniqueness of solutions of a class of fractional differential equations abstract in this paper we investigate the existence and uniqueness of solutions for the following class of multi order fractional differential equations d 1 1 1 d n n n u t i 1 n d i i i u t d i n i i u t f t u t t 0 1 u 0 0 i 1 n i 1 i 0 i 0 1 i n where d i n i i denotes the generalized erdelyi kober operator of fractional derivative of order i moreover some properties concerning the positive maximal minimal and continuation of solutions are obtained

existence and uniqueness of holomorphic solutions for fractional cauchy problem by employing majorant functions the existence and uniqueness of holomorphic solutions to nonlinear fractional partial differential equations the cauchy problems are introduced furthermore the analytic continuation of solutions is studied

the controllability of fractional control systems with control delay this paper discusses the controllability of fractional control systems with control delay we firstly give the solution expression for fractional control systems with control delay then give the necessary and sufficient conditions for the controllability of fractional control systems with control delay

ae solutions and ae solvability to general interval linear systems abstract we consider linear systems of equations and inequalities with coefficients varying inside given intervals we define their solutions so called ae solutions and solvability so called ae solvability by using forall exists quantification of interval parameters we present an explicit description of the ae solutions and discuss complexity issues as well for ae solvability we propose a sufficient condition only but for a specific sub class of problems a complete characterization is developed moreover we investigate inequality systems for which ae solvability is equivalent to existence of an ae solution

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

set valued system of fractional differential equations with hysteresis in this paper we investigate the global solvability in l 1 0 1 of a set valued system of nonlinear fractional differential equations with hysteresis some existence theorems for both single and multivalued systems are proved

ae solutions to interval linear systems over max plus algebra abstract this paper introduces a concept of ae solutions to interval max plus linear systems a rather general concept which includes many known concepts of solutions to interval systems weak solutions strong solutions tolerance solutions and control solutions as its special cases we state full characterizations of ae solutions for the interval max plus systems including both linear inequalities and linear equations moreover a kind of dependency characterized by double appearance of some sub matrix of the constraint matrix is discussed and we prove that which can be relaxed with no change in ae solvability

zeroing neural network for solving time varying linear equation and inequality systems a typical recurrent neural network called zeroing neural network znn was developed for time varying problem solving in a previous study many applications result in time varying linear equation and inequality systems that should be solved in real time this paper provides a znn model for determining the solution of time varying linear equation and inequality systems by introducing a nonnegative slack variable the time varying linear equation and inequality systems are transformed into a mixed nonlinear system the znn model is established via the definition of an indefinite error function and the usage of an exponential decay formula theoretical results indicate the convergence property of the proposed znn model comparative simulation results prove the znn effectiveness and superiority for time varying linear equation and inequality systems furthermore the proposed znn model is employed to robot manipulators thus showing the znn applicability

constrained controllability of fractional linear systems with delays in control abstract the paper presents finite dimensional dynamical control systems described by linear fractional order state equations with multiple delays in control the constrained controls are considered the set of admissible control values is assumed to be a compact set containing 0 a convex and compact set containing 0 in its interior a cone with vertex at zero and a nonempty interior or a convex and close cone with nonempty interior and vertex at zero the definitions of various types of constrained controllability of the linear fractional systems with delays in control are formulated new necessary and sufficient conditions for constrained relative controllability of fractional order control systems with delayed controls are established and proved numerical examples are provided to illustrate the obtained theoretical results

numerical simulation of the fractional bloch equations in physics and chemistry specifically in nmr nuclear magnetic resonance or mri magnetic resonance imaging or esr electron spin resonance the bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization m m x m y m z as a function of time when relaxation times t 1 and t 2 are present recently some fractional models have been proposed for the bloch equations however effective numerical methods and supporting error analyses for the fractional bloch equation fbe are still limited in this paper the time fractional bloch equations tfbe and the anomalous fractional bloch equations afbe are considered firstly we derive an analytical solution for the tfbe with an initial condition secondly we propose an effective predictor corrector method pcm for the tfbe and the error analysis for pcm is investigated furthermore we derive an effective implicit numerical method inm for the anomalous fractional bloch equations afbe and the stability and convergence of the inm are investigated we prove that the implicit numerical method for the afbe is unconditionally stable and convergent finally we present some numerical results that support our theoretical analysis

new characterizations of tolerance control and localized solutions to interval system of linear equations abstract in this paper we propose new characterizations of tolerance control and localized solutions to interval system of linear equations and apply our proposed results to represent their solution sets in terms of level sets

on generalized linear regular delay systems in this paper we study generalized linear singular delay systems such a system is reduced to a suitable homogeneous one using the kronecker canonical form the latter is decomposed into five subsystems whose solutions are obtained moreover the form of the initial function is given so that the corresponding initial value problem is considered

derivative constrained optimum broad band antenna arrays the optimization problem corresponding to the design of a presteered broadband processor with maximally flat second order spatial response in the look direction is discussed the constraints corresponding to necessary and sufficient conditions for second order flatness are presented the nonlinearly constrained optimization approach is unable to consistently locate the global minimum an approach to solving this problem that essentially converts the nonconvex optimization problem into a parameterized set of convex problems is presented in the case of 2 d scenarios the global optimum is determined by finding the roots of a cubic function the characteristics of the constraints including the minimum number required and the dependence on the choice of coordinate systems are examined

generalized linear fractional programming under interval uncertainty abstract data in many real life engineering and economical problems suffer from inexactness herein we assume that we are given some intervals in which the data can simultaneously and independently perturb we consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values the method reduces the problem to solving from two to four real valued generalized linear fractional programs which can be computed in polynomial time using an appropriate interior point method solver we consider also the inverse problem how much can data of a real generalized linear fractional program vary such that the optimal values do not exceed some prescribed bounds we propose a method for calculating often the largest possible ranges of admissible variations it needs to solve only two real valued generalized linear fractional programs we illustrate the approach on a simple von neumann economic growth model

numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis in this paper a system of nonlinear fractional differential equations fdes are considered they have been solved by legendre wavelets method combining with its operational matrix however there are no articles about solving this system using wavelets method the main purpose of this technique is to transform the initial equations into a nonlinear system of algebraic equations which can be solved easily the convergence and error analysis are presented to show the correctness and feasibility of method proposed for solving the above mentioned problem finally the applicability and efficiency of the mentioned approach are demonstrated by three numerical examples

inhomogeneous polynomial optimization over a convex set an approximation approach in this paper we consider computational methods for optimizing a multivariate inhomogeneous polynomial function over a general convex set the focus is on the design and analysis of polynomial time approximation algorithms the methods are able to deal with optimization models with polynomial objective functions in any fixed degrees in particular we first study the problem of maximizing an inhomogeneous polynomial over the euclidean ball a polynomial time approximation algorithm is proposed for this problem with an assured relative worst case performance ratio which is dependent only on the dimensions of the model the method and approximation ratio are then generalized to optimize an inhomogeneous polynomial over the intersection of a finite number of co centered ellipsoids furthermore the constraint set is extended to a general convex compact set specifically we propose a polynomial time approximation algorithm with a relative worst case performance ratio for polynomial optimization over some convex compact sets e g a polytope finally numerical results are reported revealing good practical performance of the proposed algorithms for solving some randomly generated instances

on a riemann liouville generalized taylor s formula in this paper a generalized taylor s formula of the kindfx j 0najx a j 1 1 tnx whereaj r x a 0 1 is established such expression is precisely the classical taylor s formula in the particular case 1 in addition detailed expressions fortn x andaj involving the riemann liouville fractional derivative and some applications are also given

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

center stable manifold for planar fractional damped equations in this paper we discuss the existence of a center stable manifold for planar fractional damped equations by constructing a suitable lyapunovperron operator via giving asymptotic behavior of mittagleffler function we obtain an interesting center stable manifold theorem finally an example is provided to illustrate the result

some exact solutions to stefan problems with fractional differential equations some exact solutions to the first second and extended stefan problems with fractional time derivative described in the caputo sense are given by means of fractional green s function and wright function in this paper by the aid of simple calculations many results of differential equations of integer order can be obtained as special cases of the results given by this paper

almost automorphic mild solutions to fractional differential equations abstract we introduce the concept of resolvent families to prove the existence of almost automorphic mild solutions to the differential equation d t u t a u t t n f t 1 2 n z considered in a banach space x where f r x is almost automorphic we also prove the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t 1 2 assuming f t x is almost automorphic in t for each x x satisfies a global lipschitz condition and takes values on x finally we prove also the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t u t 1 2 under analogous conditions as in the previous case

generalized fractional controller for singular systems of differential equations abstract in this article we consider a class of singular linear systems of first order and introduce a generalized fractional order feedback controller of caputo type the closed loop system in question is a singular system of differential equations having both first and fractional order derivatives we provide a comprehensive theory for the existence and uniqueness of solutions as well as for the stability of the system with inclusion of the fractional order controller an example of a singular system with a fractional order proportional integral controller as well as an example on a 3 bus power system with inclusion of a fractional order damping controller is given to illustrate our theory

numerical solution of bivariate and polyanalytic polynomial systems finding the real solutions of a bivariate polynomial system is a central problem in robotics computer modeling and graphics computational geometry and numerical optimization we propose an efficient and numerically robust algorithm for solving bivariate and polyanalytic polynomial systems using a single generalized eigenvalue decomposition in contrast to existing eigen based solvers the proposed algorithm does not depend on grobner bases or normal sets nor does it require computing eigenvectors or solving additional eigenproblems to recover the solution the method transforms bivariate systems into polyanalytic systems and then uses resultants in a novel way to project the variables onto the real plane associated with the two variables solutions are returned counting multiplicity and their accuracy is maximized by means of numerical balancing and newton raphson refinement numerical experiments show that the proposed algorithm consistently recovers a higher percentage of solutions and is at the sa

necessary and sufficient conditions for unified optimality of interval linear program in the general form abstract this paper considers optimal solutions of general interval linear programming problems the most general concepts of optimal solutions are introduced in a unified framework the existing optimal solution concepts of interval linear program such as weak and strong optimal solutions are all the special cases in this framework necessary and sufficient conditions for checking a class of optimality are developed according to the kkt conditions also the comparison among several conclusions using kkt conditions and tangent core technique in various forms of interval linear programming is proposed

on cauchy problem for nonlinear fractional differential equation with random discrete data abstract this paper is concerned with finding the solution u x t of the cauchy problem for nonlinear fractional elliptic equation with perturbed input data this study shows that our forward problem is severely ill posed in sense of hadamard for this ill posed problem the trigonometric of non parametric regression associated with the truncation method is applied to construct a regularized solution under prior assumptions for the exact solution the convergence rate is obtained in both l2 and h q for q 0 norm moreover the numerical example is also investigated to justify our results

controllability and observability of impulsive fractional linear time invariant system in this paper we deal with the controllability and observability of impulsive fractional linear time invariant if lti for short system our main purpose is to built some necessary and sufficient conditions of controllability and observability for the if lti system at the same time we establish some conclusions of controllability and observability for a continuous fractional lti system which is a special case of the if lti system examples are given to illustrate our results

on the maximization of a concave quadratic function with box constraints a new method for maximizing a concave quadratic function with bounds on the variables is introduced the new algorithm combines conjugate gradients with gradient projection techniques as the algorithm of more and toraldo siam j optimization 1 1991 pp 93 113 and other well known methods do a new strategy for the decision of leaving the current face is introduced that makes it possible to obtain finite convergence even for a singular hessian and in the presence of dual degeneracy numerical experiments are presented

farkas type conditions of general interval linear systems for ae solvability abstract we present farkas type necessary and sufficient conditions for ae solvability of two specific general interval linear systems we generalize the farkas type theorems of interval linear systems to a unified framework moreover each particular previously published result of farkas type condition of interval linear systems is a special case of our general approach

weak and strong solvability of interval linear systems of equations and inequalities abstract we consider weak and strong solvability of general interval linear systems consisting of mixed equations and inequalities with mixed free and sign restricted variables we generalize the well known weak solvability characterizations by oettli prager for equations and gerlach for inequalities to a unified framework in the same manner we extend strong solvability theorems to general interval linear systems next we propose a sufficient condition for checking strong solvability we give an application in linear programming with interval data by means of weak and strong solvability we determine limits of the optimal values for any form of the problem setting

global minimization of normal quartic polynomials based on global descent directions a normal quartic polynomial is a quartic polynomial whose fourth degree term coefficient tensor is positive definite its minimization problem is one of the simplest cases of nonconvex global optimization and has engineering applications we call a direction a global descent direction of a function at a point if there is another point with a lower function value along this direction for a normal quartic polynomial we present a criterion to find a global descent direction at a noncritical point a saddle point or a local maximizer we give sufficient conditions to judge whether a local minimizer is global and give a method for finding a global descent direction at a local but not global minimizer we also give a formula at a critical point and a method at a noncritical point to find a one dimensional global minimizer along a global descent direction based upon these we propose a global descent algorithm for finding a global minimizer of a normal quartic polynomial when n 2 for the case n ge 3 we propose an algorithm for finding an epsilon global minimizer at each iteration of a second algorithm a system of constrained nonlinear equations is solved numerical tests show that these two algorithms are promising

optimality conditions and optimization methods for quartic polynomial optimization abstract in this paper multivariate quartic polynomial optimization program qpop is considered quartic optimization problems arise in various practical applications and are proved to be np hard we discuss necessary global optimality conditions for quartic problem qpop and then we present a new strongly or e strongly local optimization method according to necessary global optimality conditions which may escape and improve some kkt points finally we design a global optimization method for problem qpop by combining the new strongly or e strongly local optimization method and an auxiliary function numerical examples show that our algorithms are efficient and stable

on computing the maximal delay intervals for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems the authors consider delay systems of both retarded and neutral types expressed in state space forms the author s main goal is to provide a computation oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability the author s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency dependent matrices based on these results the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems the author s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units

some results of the degenerate fractional differential system with delay an analytic study on linear systems of degenerate fractional differential equations with constant coefficients is presented we discuss the existence and uniqueness of solutions for the initial value problem of linear degenerate fractional differential systems the exponential estimation of the degenerate fractional differential system with delay and sufficient conditions for the finite time stability for the system are obtained finally an example is provided to illustrate the effectiveness of the presented analytical approaches

localized solutions to interval linear equations in this paper we propose a new type of solutions localized solutions to interval linear equations ax b the new solutions are based on l localized solutions and r localized solutions the concepts of the three solutions are given and the characteristics of the new solutions to the interval linear equations are described by means of nonlinear inequality as is similar to the well known oettli prager inequality which is related to the mid point and interval radius some necessary conditions of the three types of solutions to the equations are given

dynamical analysis of fractional order modified logistic model in this paper we study a fractional differential equation model of the single species multiplicative allee effect first we study the stability of equilibrium points further we give some sufficient conditions ensuring the existence and uniqueness of integral solution in the last section we perform several numerical simulations to validate our analytical findings

caputo and related fractional derivatives in singular systems abstract by using the caputo c fractional derivative and two recently defined alternative versions of this derivative the caputo fabrizio cf and the atangana baleanu ab fractional derivative firstly we focus on singular linear systems of fractional differential equations with constant coefficients that can be non square matrices or square singular we study existence of solutions and provide formulas for the case that there do exist solutions then we study the existence of unique solution for given initial conditions several numerical examples are given to justify our theory

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

a note on property of the mittag leffler function abstract recently the authors have found in some publications that the following property 0 1 of mittag leffler function is taken for granted and used to derive other properties 0 1 e a t s e a t e a s t s 0 where a is a real constant and 0 in this note it is proved that the above property is unavailable unless 1 or a 0 moreover a new equality on e a t is developed whose limit state as 1 is just the property 0 1

exact and discretized stability of the bagley torvik equation abstract the paper discusses stability and asymptotic properties of a two term linear fractional differential equation involving the bagley torvik equation as the particular case these properties are analysed for the exact as well as numerical solutions obtained from the grunwald letnikov discretization of the studied differential equation as the main results precise descriptions of the exact and discretized stability regions are presented including the decay rate of the solutions these results enable us among others to observe similarities and distinctions between the asymptotic behaviour of the classical and fractional damping models

regularization of linear descriptor systems with variable coefficients we study linear descriptor control systems with rectangular variable coefficient matrices we introduce condensed forms for such systems under equivalence transformations and use these forms to detect whether the system can be transformed to a uniquely solvable closed loop system via state or derivative feedback we show that under some mild assumptions every such system consists of an underlying square subsystem that behaves essentially like a standard state space system plus some solution components that are constrained to be zero

on systems of linear fractional differential equations with constant coefficients abstract this paper deals with the study of linear systems of fractional differential equations such as the following system 1 y a x y b x where y is the riemann liouville or the caputo fractional derivative of order 0 2 a x a 11 x a 1 n x a n 1 x a nn x b x b 1 x b n x are matrices of known real functions in a way analogous to the usual case we show how a generalized matrix exponential function and certain fractional green function in connection with the mittag leffler type functions would allow us to obtain an explicit representation of the general solution to the system 1 when a is a constant matrix

technical communique stabilization of discrete time singular systems a matrix inequalities approach this paper is concerned with the state feedback stabilization problem of discrete time singular systems the singular system under consideration is not assumed to be regular the problem we address is to design state feedback controllers such that the resulting closed loop system is regular causal and stable conditions for the existence of solutions to this problem are obtained expressed in terms of certain matrix inequalities when these conditions are satisfied the explicit formula of desired state feedback controllers is also given without resorting to decomposing the system matrices

solvability and feasibility of interval linear equations and inequalities abstract this paper considers solvability and feasibility of interval linear equations and inequalities the new concepts of solvability and feasibility are introduced in a unified framework some existing concepts such as weak solvability strong solvability weak feasibility and strong feasibility are special cases in this framework necessary and sufficient conditions for checking new types of solvability and feasibility are developed

numerical solution of fractional integro differential equations by a hybrid collocation method fractional integro differential equations have been recently solved by many methods such as adomian decomposition method differential transform method collocation method and taylor expansion approach in this paper a hybrid collocation method is used which combines a non polynomial collocation used on the first subinterval and graded piecewise polynomial collocation used on the rest of the interval a theoretical analysis for the convergence order of the method is presented some numerical examples are given which confirm the theoretical results

fractional order nonlinear systems with delay in iterative learning control in this paper we discuss a p type iterative learning control ilc scheme for a class of fractional order nonlinear systems with delay by introducing the norm and using gronwall inequality the sufficient condition for the robust convergence of the tracking errors is obtained based on this convergence the p type ilc updating laws can be determined

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

on stable manifolds for planar fractional differential equations in this paper we establish a local stable manifold theorem near a hyperbolic equilibrium point for planar fractional differential equations the construction of this stable manifold is based on the associated lyapunov perron operator an example is provided to illustrate the result

on mittag leffler type functions in fractional evolution processes abstract we review a variety of fractional evolution processes so defined being governed by equations of fractional order whose solutions turn out to be related to mittag leffler type functions the chosen equations are the simplest of the fractional calculus and include the abel integral equations of the second kind which are relevant in typical inverse problems and the fractional differential equations which govern generalized relaxation and oscillation phenomena

approximation algorithms for homogeneous polynomial optimization with quadratic constraints in this paper we consider approximation algorithms for optimizing a generic multi variate homogeneous polynomial function subject to homogeneous quadratic constraints such optimization models have wide applications e g in signal processing magnetic resonance imaging mri data training approximation theory and portfolio selection since polynomial functions are non convex the problems under consideration are all np hard in general in this paper we shall focus on polynomial time approximation algorithms in particular we first study optimization of a multi linear tensor function over the cartesian product of spheres we shall propose approximation algorithms for such problem and derive worst case performance ratios which are shown to be dependent only on the dimensions of the model the methods are then extended to optimize a generic multi variate homogeneous polynomial function with spherical constraint likewise approximation algorithms are proposed with provable approximation performance ratios furthermore the constraint set is relaxed to be an intersection of co centered ellipsoids namely we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin and propose polynomial time approximation algorithms with provable worst case performance ratios numerical results are reported illustrating the effectiveness of the approximation algorithms studied