Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative

Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative

In this paper, we establish the existence and uniqueness of solution for a nonlinear coupled system of implicit fractional differential equations including ψ-Caputo fractional operator under nonlocal conditions. Schaefer's and Banach fixed-point theorems are applied to obtain the solvability re...

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Main Author: Tamer Nabil
Format: Article
Language:English
Published: AIMS Press 2021-03-01
Series:AIMS Mathematics
Subjects:
fixed-point
ψ-caputo operator
coupled implicit system
ulam stability
existence of solution
Online Access:http://www.aimspress.com/article/doi/10.3934/math.2021301?viewType=HTML
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spelling doaj-93e5a0af9f3d442c8f0404c4fbb25d9b2021-03-16T01:26:46ZengAIMS PressAIMS Mathematics2473-69882021-03-01655088510510.3934/math.2021301Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivativeTamer Nabil01 King Khalid University, College of Science, Department of Mathematics, Abha, Saudi Arabia 2 Suez Canal University, Faculty of Computers and Informatics, Department of Basic Science, Ismailia, EgyptIn this paper, we establish the existence and uniqueness of solution for a nonlinear coupled system of implicit fractional differential equations including ψ-Caputo fractional operator under nonlocal conditions. Schaefer's and Banach fixed-point theorems are applied to obtain the solvability results for the proposed system. Furthermore, we extend the results to investigate several types of Ulam stability for the proposed system by using classical tool of nonlinear analysis. Finally, an example is provided to illustrate the abstract results.http://www.aimspress.com/article/doi/10.3934/math.2021301?viewType=HTMLfixed-pointψ-caputo operatorcoupled implicit systemulam stabilityexistence of solution
collection DOAJ
language English
format Article
sources DOAJ
author Tamer Nabil
spellingShingle Tamer Nabil
Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative
AIMS Mathematics
fixed-point
ψ-caputo operator
coupled implicit system
ulam stability
existence of solution
author_facet Tamer Nabil
author_sort Tamer Nabil
title Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative
title_short Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative
title_full Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative
title_fullStr Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative
title_full_unstemmed Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative
title_sort ulam stabilities of nonlinear coupled system of fractional differential equations including generalized caputo fractional derivative
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2021-03-01
description In this paper, we establish the existence and uniqueness of solution for a nonlinear coupled system of implicit fractional differential equations including ψ-Caputo fractional operator under nonlocal conditions. Schaefer's and Banach fixed-point theorems are applied to obtain the solvability results for the proposed system. Furthermore, we extend the results to investigate several types of Ulam stability for the proposed system by using classical tool of nonlinear analysis. Finally, an example is provided to illustrate the abstract results.
topic fixed-point
ψ-caputo operator
coupled implicit system
ulam stability
existence of solution
url http://www.aimspress.com/article/doi/10.3934/math.2021301?viewType=HTML
work_keys_str_mv AT tamernabil ulamstabilitiesofnonlinearcoupledsystemoffractionaldifferentialequationsincludinggeneralizedcaputofractionalderivative
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