On Nonlinear Periodic Problems with Caputo’s Exponential Fractional Derivative – Advances in the theory of nonlinear analysis and its applications

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Original research article

On Nonlinear Periodic Problems with Caputo's Exponential Fractional Derivative

Author(s):

Mohamed Chohri^a, Soufyane Bouriah^b, Abdelkrim Salim^c, Mouffak Benchohra^d

^a Department of Mathematics, University of Oran1 Ahmed Ben Bella, Oran, Algeria.
^b Department of Mathematics, University Hassiba Benbouali of Chlef, Chlef, Algeria.
^c Faculty of Technology, Hassiba Benbouali University, Chlef, Algeria; Laboratory of Mathematics, University of Sidi Bel-Abbes, Bel-Abbes, Algeria.
^d Laboratory of Mathematics, University of Sidi Bel-Abbes, Bel-Abbes, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 7(1), 103-120.

Received: June 14, 2022

Accepted: November 28, 2022

Published: December 3, 2022

Abstract

In this article, we employ Mawhin’s theory of degree of coincidence to provide an existence result for a class of problems involving nonlinear implicit fractional differential equations with the exponentially fractional derivative of Caputo. Two examples are provided to demonstrate the applicability of our results.

Keywords: Caputo’s exponential fractional derivative, implicit fractional differential equations, fractional integral, existence, coincidence degree theory.

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APA Style

Chohri, M., Bouriah, S., Abdelkrim, S., & Benchohra, M. (2023). On Nonlinear Periodic Problems with Caputo’s Exponential Fractional Derivative. Advances in the Theory of Nonlinear Analysis and its Application, 7(1), 103-120.