Numerical solution of fractional boundary value problem with caputo-fabrizio and its fractional integral

M Moumen Bekkouche; I Mansouri; A A Azeb Ahmed

doi:10.1007/s12190-022-01708-z

Numerical solution of fractional boundary value problem with caputo-fabrizio and its fractional integral

J Appl Math Comput. 2022;68(6):4305-4316. doi: 10.1007/s12190-022-01708-z. Epub 2022 Feb 4.

Authors

M Moumen Bekkouche¹, I Mansouri¹, A A Azeb Ahmed¹

Affiliation

¹ Department of Mathematics, Faculty of Exact Sciences, El Oued University, 39000 El Oued, Algeria.

Abstract

In this article, we investigate the existence and uniqueness of the solution of a fractional boundary value problem with conformable fractional derivation of the Caputo-Fabrizio type. In order to study this problem we used a new definition of fractional integral as an inverse of the conformable fractional derivative of Caputo-Fabrizio, therefore, so we transformed the problem to a equivalent linear Volterra-Fredholm integral equations of the second kind, and taking sufficient conditions existence and uniqueness of this solution is proven based on the results obtained. The analytical study is followed by a complete numerical study.

Keywords: Caputo-Fabrizio fractional derivative; Fractional boundary value problem; Fractional integral; Volterra-Fredholm integral equation.