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

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

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