EXISTENCE AND UNIQUENESS OF SOLUTION OF DIFFERENTIAL EQUATION OF FRACTIONAL ORDER VIA S-ITERATION

In this paper, we study the existence, uniqueness and other properties of solutions of differential equation of fractional order involving the Caputo fractional derivative. The tool employed in the analysis is based on application of S− iteration method. The study of qualitative properties in general required differential and integral inequalities, and here S−iteration method itself has equally important contribution to study various properties such as dependence on initial data, closeness of solutions and dependence on parameters and functions involved therein. Finally, we present an example in support of all proved results

Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition

summary:The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions