An extension of the Picard theorem to fractional differential equations with a Caputo-Fabrizio derivative
type: Item
instance of: scholarly article
title: An extension of the Picard theorem to fractional differential equations with a Caputo-Fabrizio derivative
zbMATH Open document ID: 1469.34020
DOI: 10.1155/2021/6624861
author: H. R. Marasi
author: A. Soltani Joujehi
author: Hassen Aydi
published in: Journal of Function Spaces
publication date: 2021-05-07T00:00:00Z
review text: In this paper, fractional differential equations described by the fractional operator with exponential kernel are considered. The present operator is known as the Caputo-Fabrizio derivative. The paper addresses the problem of the existence and uniqueness of the solution of the fractional differential equation. The classical Picard-Lindelöf theorem used to prove the existence and uniqueness of differential equations with integer-order derivatives is recalled and extended in the context of fractional differential equations. One of the main novelty in this paper concerns the method used to obtain the solutions of the fractional differential equations. The recursive approximation method has been used. The procedure for obtaining the solutions of fractional differential equations recursively is illustrated via an example to support the paper's results.
reviewed by: Ndolane Sene
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 7345479
zbMATH Keywords: fractional differential equations
zbMATH Keywords: Caputo-Fabrizio derivative
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: fractional calculus
Wikidata QID: Q115243657
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6624861
OpenAlex ID: W3138518645
cites work: Q5699297
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description: scientific article; zbMATH DE number 7345479