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

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 frac...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2022, Vol.68 (6), p.4305-4316
Main Authors: Moumen Bekkouche, M., Mansouri, I., Ahmed, A. A. Azeb
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary value problems
Computational Mathematics and Numerical Analysis
Derivatives
Fractional calculus
Fredholm equations
Integral equations
Integrals
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Theory of Computation
Uniqueness
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Summary: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.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-022-01708-z