The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators

Boutiara A., Etemad S., Hussain A., 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/s13662-021-03253-8
  • 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: Coupled system, Fixed point, The Ulam–Hyers stability, φ-Caputo fractional operator
  • Uşak University Affiliated: No

Abstract

We investigate the existence and uniqueness of solutions to a coupled system of the hybrid fractional integro-differential equations involving φ-Caputo fractional operators. To achieve this goal, we make use of a hybrid fixed point theorem for a sum of three operators due to Dhage and also the uniqueness result is obtained by making use of the Banach contraction principle. Moreover, we explore the Ulam–Hyers stability and its generalized version for the given coupled hybrid system. An example is presented to guarantee the validity of our existence results.