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

Boutiara A., Etemad S., Alzabut J., Hussain A., Subramanian M., Rezapour S.

Advances in Difference Equations, vol.2021, no.1, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03525-3
  • Journal Name: Advances in Difference Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Existence-uniqueness, Fixed point, Fractional q-difference equation, q-operators
  • Uşak University Affiliated: No

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.