Ulam stabilities of nonlinear coupled system of fractional differential equations including generalized Caputo fractional derivative

• Published in: AIMS mathematics Vol. 6; no. 5; pp. 5088 - 5105
• Main Author: Nabil, Tamer
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2021
• Subjects: coupled implicit system; existence of solution; fixed-point; ulam stability; ψ-caputo operator
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021301

In this paper, we establish the existence and uniqueness of solution for a nonlinear coupled system of implicit fractional differential equations including ψ-Caputo fractional operator under nonlocal conditions. Schaefer's and Banach fixed-point theorems are applied to obtain the solvability results for the proposed system. Furthermore, we extend the results to investigate several types of Ulam stability for the proposed system by using classical tool of nonlinear analysis. Finally, an example is provided to illustrate the abstract results.