An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative-Reference-Cited by-同舟云学术

An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

Published:2021-03-15 Issue: Volume:2021 Page:1-6
ISSN:2314-8888
Container-title:Journal of Function Spaces
language:en
Short-container-title:Journal of Function Spaces

Author:

Marasi H. R.¹^ORCID,Joujehi A. Soltani¹,Aydi H.²³⁴^ORCID

Affiliation:

1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

2. Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia

3. China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

4. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Abstract

In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2021/6624861.pdf

Reference31 articles.

1. Geometric and physical interpretation of fractional integration and fractional differentiation;I. Podlubny;Fractional Calculus and Applied Analysis,2002

2. Linear Models of Dissipation whose Q is almost Frequency Independent--II

3. A new definition of fractional derivative without singular kernel;M. Caputo;Progress in Fractional Differentiation and Applications,2015

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