Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions

Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions

Abstract In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equations. Using classical fixed point theorems, we develop the required conditions. Furth...

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Main Authors: Asma, Arshad Ali, Kamal Shah, Fahd Jarad
Format: Article
Language:English
Published: SpringerOpen 2019-01-01
Series:Advances in Difference Equations
Subjects:
Impulsive conditions
Implicit differential equations
Ulam–Hyers stability
Online Access:http://link.springer.com/article/10.1186/s13662-018-1943-x
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spelling doaj-c9b6356651ba43b1940a22e6a612841a2020-11-25T00:51:53ZengSpringerOpenAdvances in Difference Equations1687-18472019-01-012019112710.1186/s13662-018-1943-xUlam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditionsAsma0Arshad Ali1Kamal Shah2Fahd Jarad3Department of Mathematics, COMSATS University IslamabadDepartment of Mathematics, University of MalakandDepartment of Mathematics, University of MalakandDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya UniversityAbstract In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equations. Using classical fixed point theorems, we develop the required conditions. Further, using the techniques of nonlinear functional analysis, we investigate Ulam–Hyers stability results to the proposed problem. For applications of our derived results, we present two numerical examples.http://link.springer.com/article/10.1186/s13662-018-1943-xImpulsive conditionsImplicit differential equationsUlam–Hyers stability
collection DOAJ
language English
format Article
sources DOAJ
author Asma
Arshad Ali
Kamal Shah
Fahd Jarad
spellingShingle Asma
Arshad Ali
Kamal Shah
Fahd Jarad
Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
Advances in Difference Equations
Impulsive conditions
Implicit differential equations
Ulam–Hyers stability
author_facet Asma
Arshad Ali
Kamal Shah
Fahd Jarad
author_sort Asma
title Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
title_short Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
title_full Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
title_fullStr Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
title_full_unstemmed Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
title_sort ulam–hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2019-01-01
description Abstract In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equations. Using classical fixed point theorems, we develop the required conditions. Further, using the techniques of nonlinear functional analysis, we investigate Ulam–Hyers stability results to the proposed problem. For applications of our derived results, we present two numerical examples.
topic Impulsive conditions
Implicit differential equations
Ulam–Hyers stability
url http://link.springer.com/article/10.1186/s13662-018-1943-x
work_keys_str_mv AT asma ulamhyersstabilityanalysistoaclassofnonlinearimplicitimpulsivefractionaldifferentialequationswiththreepointboundaryconditions
AT arshadali ulamhyersstabilityanalysistoaclassofnonlinearimplicitimpulsivefractionaldifferentialequationswiththreepointboundaryconditions
AT kamalshah ulamhyersstabilityanalysistoaclassofnonlinearimplicitimpulsivefractionaldifferentialequationswiththreepointboundaryconditions
AT fahdjarad ulamhyersstabilityanalysistoaclassofnonlinearimplicitimpulsivefractionaldifferentialequationswiththreepointboundaryconditions
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