Yong-Kui Chang

Some new existence results for fractional differential inclusions with boundary conditions

This paper is mainly concerned with the existence of solutions for a certain class of fractional differential inclusions with boundary conditions. By using Bohnenblust-Karlins fixed point theorem, a main existence theorem is obtained. As an application of this main theorem, we establish two existence results when the multi-valued nonlinearity F has sub-linear or linear growth in the state variable y. Our results are even new when applied to a corresponding single-valued problem.

Existence of Solutions for Impulsive Neutral Integro-Differential Inclusions with Nonlocal Initial Conditions via Fractional Operators

This paper is mainly concerned with existence of mild solutions for first-order impulsive neutral integro-differential inclusions with nonlocal initial conditions in α-norm. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multivalued maps, a main existence theorem is established. As an application of this main theorem, a practical consequence is derived for the sublinear growth case. Finally, we present an application to a neutral partial integro-differential equation with Dirichlet and nonlocal initial conditions.

Solvability of impulsive neutral evolution differential inclusions with state-dependent delay

In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has sub-linear growth in the state variable.

Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.

Almost Periodic and Pseudo Almost Periodic Mild Solutions to a Partial Differential Equation VIA Fractional Operators

This article is mainly concerned with the existence and uniqueness of almost periodic and pseudo almost periodic mild solutions to a class of partial differential equations in Banach spaces. Under some reasonable assumptions, the main results are proved in α-norm. Our results cover the cases that the functions F 1; F 2 take values in different spaces such as X, X α, and X ß, where α ≤ β ∈ (0; 1).