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Positive solutions for nonlinear Caputo-Hadamard fractional relaxation differential equations

Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria

Applied Mathematics Lab., Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba, 23000, Algeria

* Corresponding Author
Annals of Communications in Mathematics 2021
, 4 (3),
226-236.
https://doi.org/10.62072/acm.2021.040302
Received: 4 August 2021 |
Accepted: 13 December 2021 |
Published: 31 December 2021

Abstract

We study the existence and uniqueness of positive solutions of the nonlinear
fractional relaxation differential equation where Dα/1 is the Caputo-Hadamard fractional derivative of order 0 < α ≤ 1. In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.

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Cite This Article

Positive solutions for nonlinear Caputo-Hadamard fractional relaxation differential equations.

Annals of Communications in Mathematics,

2021,
4 (3):
226-236.
https://doi.org/10.62072/acm.2021.040302
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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