A Sequential Differential Problem With Caputo and Riemann Liouville Derivatives Involving Convergent Series

Abstract

In this paper, we study a new nonlinear sequential differential prob- lem with nonlocal integral conditions that involve convergent series. The problem involves two fractional order operators: Riemann-Liouville inte- gral, Caputo and Riemann-Liouville derivatives. We prove an existence and uniqueness result. Also, we prove a new existence result. We end our paper by presenting some illustrative examples.