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

Authors : Yazid GOUARİ, Mahdi RAKAH, Zoubir DAHMANİ

Pages : 319-335

Doi:10.31197/atnaa.1224234

View : 56 | Download : 98

Publication Date : 2023-07-23

Article Type : Research Paper

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