On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations

A generalized proportional vector-order fractional derivative in the Caputo sense is defined and studied. Two types of existence results for the mild solutions of the initial value problem for nonlinear Caputo-type generalized proportional vector-order fractional differential equations are obtained....

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Autores principales:	Mohamed I. Abbas, Snezhana Hristova
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	vector-order fractional derivatives generalized proportional fractional derivatives Leray–Schauder nonlinear alternative Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8cf934cfd7ee49cfb7dceb09bd24e161
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spelling	oai:doaj.org-article:8cf934cfd7ee49cfb7dceb09bd24e1612021-11-11T18:16:29ZOn the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations10.3390/math92127202227-7390https://doaj.org/article/8cf934cfd7ee49cfb7dceb09bd24e1612021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2720https://doaj.org/toc/2227-7390A generalized proportional vector-order fractional derivative in the Caputo sense is defined and studied. Two types of existence results for the mild solutions of the initial value problem for nonlinear Caputo-type generalized proportional vector-order fractional differential equations are obtained. With the aid of the Leray–Schauder nonlinear alternative and the Banach contraction principle, the main results are established. In the case of a local Lipschitz right hand side part function, the existence of a bounded mild solution is proved. Some examples illustrating the main results are provided.Mohamed I. AbbasSnezhana HristovaMDPI AGarticlevector-order fractional derivativesgeneralized proportional fractional derivativesLeray–Schauder nonlinear alternativeMathematicsQA1-939ENMathematics, Vol 9, Iss 2720, p 2720 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	vector-order fractional derivatives generalized proportional fractional derivatives Leray–Schauder nonlinear alternative Mathematics QA1-939
spellingShingle	vector-order fractional derivatives generalized proportional fractional derivatives Leray–Schauder nonlinear alternative Mathematics QA1-939 Mohamed I. Abbas Snezhana Hristova On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
description	A generalized proportional vector-order fractional derivative in the Caputo sense is defined and studied. Two types of existence results for the mild solutions of the initial value problem for nonlinear Caputo-type generalized proportional vector-order fractional differential equations are obtained. With the aid of the Leray–Schauder nonlinear alternative and the Banach contraction principle, the main results are established. In the case of a local Lipschitz right hand side part function, the existence of a bounded mild solution is proved. Some examples illustrating the main results are provided.
format	article
author	Mohamed I. Abbas Snezhana Hristova
author_facet	Mohamed I. Abbas Snezhana Hristova
author_sort	Mohamed I. Abbas
title	On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
title_short	On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
title_full	On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
title_fullStr	On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
title_full_unstemmed	On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations
title_sort	on the initial value problems for caputo-type generalized proportional vector-order fractional differential equations
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8cf934cfd7ee49cfb7dceb09bd24e161
work_keys_str_mv	AT mohamediabbas ontheinitialvalueproblemsforcaputotypegeneralizedproportionalvectororderfractionaldifferentialequations AT snezhanahristova ontheinitialvalueproblemsforcaputotypegeneralizedproportionalvectororderfractionaldifferentialequations
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On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations

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