Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, exist...

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Main Authors: Zeeshan Ali, Poom Kumam, Kamal Shah, Akbar Zada
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Mathematics
Subjects:
Caputo fractional derivative
implicit differential equation
Green’s function
implicit coupled system
existence theory
Ulam stability
Online Access:https://www.mdpi.com/2227-7390/7/4/341
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spelling doaj-e7a24872496a466ab6873858c1f788c02020-11-24T22:19:07ZengMDPI AGMathematics2227-73902019-04-017434110.3390/math7040341math7040341Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential EquationsZeeshan Ali0Poom Kumam1Kamal Shah2Akbar Zada3Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, PakistanCenter of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandDepartment of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18800, PakistanDepartment of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, PakistanThis manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.https://www.mdpi.com/2227-7390/7/4/341Caputo fractional derivativeimplicit differential equationGreen’s functionimplicit coupled systemexistence theoryUlam stability
collection DOAJ
language English
format Article
sources DOAJ
author Zeeshan Ali
Poom Kumam
Kamal Shah
Akbar Zada
spellingShingle Zeeshan Ali
Poom Kumam
Kamal Shah
Akbar Zada
Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations
Mathematics
Caputo fractional derivative
implicit differential equation
Green’s function
implicit coupled system
existence theory
Ulam stability
author_facet Zeeshan Ali
Poom Kumam
Kamal Shah
Akbar Zada
author_sort Zeeshan Ali
title Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations
title_short Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations
title_full Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations
title_fullStr Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations
title_full_unstemmed Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations
title_sort investigation of ulam stability results of a coupled system of nonlinear implicit fractional differential equations
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-04-01
description This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.
topic Caputo fractional derivative
implicit differential equation
Green’s function
implicit coupled system
existence theory
Ulam stability
url https://www.mdpi.com/2227-7390/7/4/341
work_keys_str_mv AT zeeshanali investigationofulamstabilityresultsofacoupledsystemofnonlinearimplicitfractionaldifferentialequations
AT poomkumam investigationofulamstabilityresultsofacoupledsystemofnonlinearimplicitfractionaldifferentialequations
AT kamalshah investigationofulamstabilityresultsofacoupledsystemofnonlinearimplicitfractionaldifferentialequations
AT akbarzada investigationofulamstabilityresultsofacoupledsystemofnonlinearimplicitfractionaldifferentialequations
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