- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 2
- A Sequential Differential Problem With Caputo and Riemann Liouville Derivatives Involving Convergent...
A Sequential Differential Problem With Caputo and Riemann Liouville Derivatives Involving Convergent Series
Authors : Yazid Gouari, Mahdi Rakah, Zoubir Dahmani
Pages : 319-335
Doi:10.31197/atnaa.1224234
View : 52 | Download : 95
Publication Date : 2023-07-23
Article Type : Research Article
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