Abstract In this paper we prove the existence of solutions for a boundary value nonlinear neutral integrodifferential problem in Rn defined on an unbounded interval. The result is obtained by using the Schaefer fixed point theorem and by using a recent result [4] on compactness of a continuous operator K : BC(I,Rn) → BC(I,Rn); here BC(I,Rn) is the Banach space of continuous functions from the (...

In the last two decades, the theory of fractional calculus has gained importance and popularity, due to its wide range of applications in varied fields of sciences and engineering as viscoelasticity, electrochemistry of corrosion, chemical physics, optics and signal processing, and so on. The main object of this paper is to provide sufficient conditions for the existence of mild solutions for a...

This paper presents a new class of boundary value problems integrodifferential fractional equations different order equipped with coupled anti-periodic and nonlocal integral conditions. We prove the existence uniqueness criteria solutions by using Leray-Schauder alternative Banach contraction mapping principle. Examples are constructed for illustration our results.

We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract resul...