Nonlinear fractional Caputo-Langevin equation with nonlocal Riemann-Liouville fractional integral conditions

Abstract

In this paper, we study the existence and uniqueness of solution for a problem consisting of a sequential nonlinear fractional Caputo-Langevin equation with nonlocal Riemann-Liouville fractional integral conditions. A variety of fixed point theorems, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder degree theory, are used. Examples illustrating the obtained results are also presented. MSC:26A33, 34A08, 34B10.