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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Veröffentlicht in:Advances in difference equations Jg. 2021; H. 1; S. 1 - 23
Hauptverfasser: Boutiara, Abdelatif, Etemad, Sina, Alzabut, Jehad, Hussain, Azhar, Subramanian, Muthaiah, Rezapour, Shahram
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 06.08.2021
Springer Nature B.V
SpringerOpen
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03525-3