On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria

On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria

Abstract In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditi...

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Main Authors: Abdelatif Boutiara, Sina Etemad, Jehad Alzabut, Azhar Hussain, Muthaiah Subramanian, Shahram Rezapour
Format: Article
Language:English
Published: SpringerOpen 2021-08-01
Series:Advances in Difference Equations
Subjects:
q-operators
Fixed point
Fractional q-difference equation
Existence-uniqueness
Online Access:https://doi.org/10.1186/s13662-021-03525-3
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spelling doaj-e498ecfa28074eb0a2e9b18822b077612021-08-08T11:09:31ZengSpringerOpenAdvances in Difference Equations1687-18472021-08-012021112310.1186/s13662-021-03525-3On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteriaAbdelatif Boutiara0Sina Etemad1Jehad Alzabut2Azhar Hussain3Muthaiah Subramanian4Shahram Rezapour5Laboratory of Mathematics and Applied Sciences, University of GhardaiaDepartment of Mathematics, Azarbaijan Shahid Madani UniversityDepartment of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, University of SargodhaDepartment of Mathematics, KPR Institute of Engineering and TechnologyDepartment of Mathematics, Azarbaijan Shahid Madani UniversityAbstract In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditions of the existence and uniqueness of solutions to a given Caputo fractional q-difference boundary value problem. Some pure techniques based on condensing operators and Sadovskii’s measure and the eigenvalue of an operator are employed to prove the main results. Also, the Ulam–Hyers stability and generalized Ulam–Hyers stability are investigated. We examine our results by providing two illustrative examples.https://doi.org/10.1186/s13662-021-03525-3q-operatorsFixed pointFractional q-difference equationExistence-uniqueness
collection DOAJ
language English
format Article
sources DOAJ
author Abdelatif Boutiara
Sina Etemad
Jehad Alzabut
Azhar Hussain
Muthaiah Subramanian
Shahram Rezapour
spellingShingle Abdelatif Boutiara
Sina Etemad
Jehad Alzabut
Azhar Hussain
Muthaiah Subramanian
Shahram Rezapour
On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
Advances in Difference Equations
q-operators
Fixed point
Fractional q-difference equation
Existence-uniqueness
author_facet Abdelatif Boutiara
Sina Etemad
Jehad Alzabut
Azhar Hussain
Muthaiah Subramanian
Shahram Rezapour
author_sort Abdelatif Boutiara
title On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
title_short On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
title_full On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
title_fullStr On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
title_full_unstemmed On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
title_sort on a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-08-01
description Abstract In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value conditions containing Riemann–Liouville fractional quantum integrals in four points. In this direction, we derive some criteria and conditions of the existence and uniqueness of solutions to a given Caputo fractional q-difference boundary value problem. Some pure techniques based on condensing operators and Sadovskii’s measure and the eigenvalue of an operator are employed to prove the main results. Also, the Ulam–Hyers stability and generalized Ulam–Hyers stability are investigated. We examine our results by providing two illustrative examples.
topic q-operators
Fixed point
Fractional q-difference equation
Existence-uniqueness
url https://doi.org/10.1186/s13662-021-03525-3
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AT jehadalzabut onanonlinearsequentialfourpointfractionalqdifferenceequationinvolvingqintegraloperatorsinboundaryconditionsalongwithstabilitycriteria
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