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

Advances in Difference Equations

Sina Etemad¹  Shahram Rezapour²  Azhar Hussain³  Abdellatif Boutiara⁴ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Department of Mathematics, University of Sargodha, 40100, Sarogodha, Pakistan;Laboratory of Mathematics and Applied Sciences, University of Ghardaia, Metlili, Algeria;

关键词: φ;    Coupled system;    Fixed point;    The Ulam–Hyers stability;    34A08;    26A33;    34A34;   

DOI  :  10.1186/s13662-021-03253-8

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY