Coupled system of $\\psi$--Caputo fractional differential equations without and with delay in generalized Banach spaces

Authors : Choukri DERBAZİ, Zidane BAİTİCHEZİDANE, Mouffak BENCHOHRA

Pages : 42-61

Doi:10.53006/rna.1007501

View : 30 | Download : 8

Publication Date : 2022-03-31

Article Type : Research Paper

Abstract :The main objective of this research manuscript is to establish various existence and uniqueness results as well as the Ulam--Hyers stability of solutions to a Coupled system of $\\psi$--Caputo fractional differential equations without and with delay in generalized Banach spaces. Existence and uniqueness results are obtained by applying Krasnoselskii\`s type fixed point theorem, Schauder\`s fixed point theorem in generalized Banach spaces, and Perov\`s fixed point theorem combined with the Bielecki norm. While Urs\`s approach is used to analyze the Ulam--Hyers stability of solutions for the proposed problem. Finally, Some examples are given to illustrate the obtained results.
Keywords : \\psi Caputo fractional derivative, Coupled system, Existence, Uniqueness, Fixed point, Bielecki norm, Ulam stability, Generalized Banach spaces