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, cilt.2021, sa.1, 2021 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2021 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1186/s13662-021-03253-8
  • Dergi Adı: Advances in Difference Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Coupled system, Fixed point, The Ulam–Hyers stability, φ-Caputo fractional operator
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.