On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones

On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones

Abstract The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is obtained by using the Banach principle. For obtaining two positive solutions, we app...

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Main Authors: Mohammed M. Matar, Manar abu Jarad, Manzoor Ahmad, Akbar Zada, Sina Etemad, Shahram Rezapour
Format: Article
Language:English
Published: SpringerOpen 2021-09-01
Series:Advances in Difference Equations
Subjects:
Boundary values problem
Fixed point
Fractional derivative
Ulam–Hyers stability
Online Access:https://doi.org/10.1186/s13662-021-03576-6
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spelling doaj-df69b6d1e16c415abd312531b2a80ebf2021-09-26T11:11:14ZengSpringerOpenAdvances in Difference Equations1687-18472021-09-012021112310.1186/s13662-021-03576-6On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on conesMohammed M. Matar0Manar abu Jarad1Manzoor Ahmad2Akbar Zada3Sina Etemad4Shahram Rezapour5Department of Mathematics, Al-Azhar University-GazaDepartment of Mathematics, Al-Azhar University-GazaDepartment of Mathematics, University of PeshawarDepartment of Mathematics, University of PeshawarDepartment of Mathematics, Azarbaijan Shahid Madani UniversityDepartment of Mathematics, Azarbaijan Shahid Madani UniversityAbstract The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is obtained by using the Banach principle. For obtaining two positive solutions, we apply another fixed point criterion due to Avery–Anderson–Henderson on cones by establishing some inequalities. An illustrative example is presented to indicate the validity of the obtained results. The results are new and provide a generalization to some known results in the literature.https://doi.org/10.1186/s13662-021-03576-6Boundary values problemFixed pointFractional derivativeUlam–Hyers stability
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed M. Matar
Manar abu Jarad
Manzoor Ahmad
Akbar Zada
Sina Etemad
Shahram Rezapour
spellingShingle Mohammed M. Matar
Manar abu Jarad
Manzoor Ahmad
Akbar Zada
Sina Etemad
Shahram Rezapour
On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones
Advances in Difference Equations
Boundary values problem
Fixed point
Fractional derivative
Ulam–Hyers stability
author_facet Mohammed M. Matar
Manar abu Jarad
Manzoor Ahmad
Akbar Zada
Sina Etemad
Shahram Rezapour
author_sort Mohammed M. Matar
title On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones
title_short On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones
title_full On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones
title_fullStr On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones
title_full_unstemmed On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery–Anderson–Henderson criterion on cones
title_sort on the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via avery–anderson–henderson criterion on cones
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-09-01
description Abstract The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is obtained by using the Banach principle. For obtaining two positive solutions, we apply another fixed point criterion due to Avery–Anderson–Henderson on cones by establishing some inequalities. An illustrative example is presented to indicate the validity of the obtained results. The results are new and provide a generalization to some known results in the literature.
topic Boundary values problem
Fixed point
Fractional derivative
Ulam–Hyers stability
url https://doi.org/10.1186/s13662-021-03576-6
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