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

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 t...

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Vydáno v:Advances in difference equations Ročník 2021; číslo 1; s. 1 - 23
Hlavní autoři: Boutiara, Abdelatif, Etemad, Sina, Alzabut, Jehad, Hussain, Azhar, Subramanian, Muthaiah, Rezapour, Shahram
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 06.08.2021
Springer Nature B.V
SpringerOpen
Témata:
Analysis
Boundary conditions
Boundary value problems
Calculus
Difference and Functional Equations
Difference equations
Eigenvalues
Existence-uniqueness
Fixed point
Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations
Fractional q-difference equation
Functional Analysis
Integrals
Investigations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
q-operators
Stability criteria
difference equation
operators
34A34
26A33
Existence-uniqueness
Fractional
Fixed point
34A08
ISSN:1687-1847, 1687-1839, 1687-1847
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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.
AbstractList 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.
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.
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.
ArticleNumber 367
Author Boutiara, Abdelatif
Subramanian, Muthaiah
Rezapour, Shahram
Alzabut, Jehad
Hussain, Azhar
Etemad, Sina
Author_xml – sequence: 1
  givenname: Abdelatif
  surname: Boutiara
  fullname: Boutiara, Abdelatif
  organization: Laboratory of Mathematics and Applied Sciences, University of Ghardaia
– sequence: 2
  givenname: Sina
  surname: Etemad
  fullname: Etemad, Sina
  organization: Department of Mathematics, Azarbaijan Shahid Madani University
– sequence: 3
  givenname: Jehad
  surname: Alzabut
  fullname: Alzabut, Jehad
  organization: Department of Mathematics and General Sciences, Prince Sultan University, Group of mathematics, Faculty of Engineering, Ostim Technical University
– sequence: 4
  givenname: Azhar
  surname: Hussain
  fullname: Hussain, Azhar
  organization: Department of Mathematics, University of Sargodha
– sequence: 5
  givenname: Muthaiah
  surname: Subramanian
  fullname: Subramanian, Muthaiah
  organization: Department of Mathematics, KPR Institute of Engineering and Technology
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  givenname: Shahram
  orcidid: 0000-0003-3463-2607
  surname: Rezapour
  fullname: Rezapour, Shahram
  email: sh.rezapour@azaruniv.ac.ir, sh.rezapour@mail.cmuh.org.tw, rezapourshahram@yahoo.ca
  organization: Department of Mathematics, Azarbaijan Shahid Madani University, Department of Medical Research, China Medical University Hospital, China Medical University
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operators
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Existence-uniqueness
Fractional
Fixed point
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SSID ssj0029488
Score 2.3562186
Snippet In this paper, we consider a nonlinear sequential q -difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value...
In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary value...
Abstract In this paper, we consider a nonlinear sequential q-difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary...
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SubjectTerms Analysis
Boundary conditions
Boundary value problems
Calculus
Difference and Functional Equations
Difference equations
Eigenvalues
Existence-uniqueness
Fixed point
Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations
Fractional q-difference equation
Functional Analysis
Integrals
Investigations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
q-operators
Stability criteria
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
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Title On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
URI https://link.springer.com/article/10.1186/s13662-021-03525-3
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Volume 2021
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