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

Year 2023, , 319 - 335, 23.07.2023

Yazid Gouari Mahdi Rakah , Zoubir Dahmani

https://doi.org/10.31197/atnaa.1224234

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.

Keywords

Caputo derivative, fixed point, Riemann-Liouville derivative, existence of solution

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