Existence for Nonautonomous Fractional Integrodifferential Equations with Nonlocal Conditions

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Existence for Delay Integrodifferential Equations of Sobolev Type with Nonlocal Conditions

This paper is concerned with delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. Using the theory of semigroups and the method of fixed points, existence results are obtained for mild solutions.

Existence of Solutions for Nonlinear Mixed Type Integrodifferential Functional Evolution Equations with Nonlocal Conditions

and Applied Analysis 3 The evolution system R t, s is said to be equicontinuous if for all bounded set Q ⊂ X, {s → R t, s x : x ∈ Q} is equicontinuous for t > 0. x ∈ C −q, b , X is said to be a mild solution of the nonlocal problem 1.1 , if x t φ t g x t for t ∈ −q, 0 , and, for t ∈ J , it satisfies the following integral equation: x t R t, 0 [ φ 0 g x 0 ] ∫ t 0 R t, s f ( s, xs, ∫ s 0 K s, r, ...

Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions

We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the pa...

Zuomao Yan EXISTENCE OF SOLUTIONS FOR SOME NONLINEAR DELAY INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

The main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii’s fixed point theorem. An example is presented in the end to show the applications of the obtain...