Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered

Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations

The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T ! R (T = R+ or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) ! R is a strictly decreasing function. We study also this problem for the vectorial Li´enard equation. We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3, 7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo recurrent) solutions of Li´enard equations (both scalar and vectorial)

Pseudo almost periodic solutions for equation with piecewise constant argument

AbstractBy using the roughness theory of exponential dichotomies and the contraction mapping, some sufficient conditions are obtained for the existence and uniqueness of pseudo almost periodic solution of the above differential equation with piecewise constant argumentdxdt=A(t)x(t)+∑j=0rAj(t)x([t−j])+g(t,x(t),x([t]),…,x([t−r]))

Structure of the Set of Bounded Solutions and Existence of Pseudo Almost Periodic Solutions of a Vector Liénard Differential Equation

International audienceWe give sufficient conditions ensuring the existence and uniqueness of pseudo almost periodic solution of the vectorial Liénard's equation

Structure of the Set of Bounded Solutions and Existence of Pseudo Almost Periodic Solutions of a Vector Liénard Differential Equation

We give sufficient conditions ensuring the existence and uniqueness of pseudo almost periodic solution of the vectorial Liénard ’s equation