Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator

In this paper, we study the existence of solutions to initial value problems for a nonlinear generalized Caputo fractional differential inclusion with Lipschitz set-valued functions. The applied fractional operator is given by the kernel kρ,s=ξρ−ξs and the derivative operator 1/ξ′ρd/dρ. The existenc...

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Autores principales:	Adel Lachouri, Abdelouaheb Ardjouni, Fahd Jarad, Mohammed S. Abdo
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/33f72e9eacf94e3f941d115a8962e497
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spelling	oai:doaj.org-article:33f72e9eacf94e3f941d115a8962e4972021-11-15T01:19:20ZSemilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator2314-888810.1155/2021/8162890https://doaj.org/article/33f72e9eacf94e3f941d115a8962e4972021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8162890https://doaj.org/toc/2314-8888In this paper, we study the existence of solutions to initial value problems for a nonlinear generalized Caputo fractional differential inclusion with Lipschitz set-valued functions. The applied fractional operator is given by the kernel kρ,s=ξρ−ξs and the derivative operator 1/ξ′ρd/dρ. The existence result is obtained via fixed point theorems due to Covitz and Nadler. Moreover, we also characterize the topological properties of the set of solutions for such inclusions. The obtained results generalize previous works in the literature, where the classical Caputo fractional derivative is considered. In the end, an example demonstrating the effectiveness of the theoretical results is presented.Adel LachouriAbdelouaheb ArdjouniFahd JaradMohammed S. AbdoHindawi LimitedarticleMathematicsQA1-939ENJournal of Function Spaces, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Adel Lachouri Abdelouaheb Ardjouni Fahd Jarad Mohammed S. Abdo Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator
description	In this paper, we study the existence of solutions to initial value problems for a nonlinear generalized Caputo fractional differential inclusion with Lipschitz set-valued functions. The applied fractional operator is given by the kernel kρ,s=ξρ−ξs and the derivative operator 1/ξ′ρd/dρ. The existence result is obtained via fixed point theorems due to Covitz and Nadler. Moreover, we also characterize the topological properties of the set of solutions for such inclusions. The obtained results generalize previous works in the literature, where the classical Caputo fractional derivative is considered. In the end, an example demonstrating the effectiveness of the theoretical results is presented.
format	article
author	Adel Lachouri Abdelouaheb Ardjouni Fahd Jarad Mohammed S. Abdo
author_facet	Adel Lachouri Abdelouaheb Ardjouni Fahd Jarad Mohammed S. Abdo
author_sort	Adel Lachouri
title	Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator
title_short	Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator
title_full	Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator
title_fullStr	Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator
title_full_unstemmed	Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator
title_sort	semilinear fractional evolution inclusion problem in the frame of a generalized caputo operator
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/33f72e9eacf94e3f941d115a8962e497
work_keys_str_mv	AT adellachouri semilinearfractionalevolutioninclusionproblemintheframeofageneralizedcaputooperator AT abdelouahebardjouni semilinearfractionalevolutioninclusionproblemintheframeofageneralizedcaputooperator AT fahdjarad semilinearfractionalevolutioninclusionproblemintheframeofageneralizedcaputooperator AT mohammedsabdo semilinearfractionalevolutioninclusionproblemintheframeofageneralizedcaputooperator
_version_	1718428975235072000

Semilinear Fractional Evolution Inclusion Problem in the Frame of a Generalized Caputo Operator

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