A study of ψ-Hilfer fractional differential system with application in financial crisis

This paper considers the fractional-order system in the sense of $\psi$-Hilfer fractional differential equations. In order to investigate the existence and uniqueness of the mild solution, the Banach contraction mapping principle and the measure of non-compactness are applied. As an application, the financial crisis model in the sense of $\psi$-Hilfer fractional differential equation will be used to prove the existence of solution and global stability of it. In addition, to illustrate the feasibility and validity of our results, the numerical simulation of the financial crisis model in the sense of Caputo will be shown in four different cases. Our results indicate that for non-integer order, the system behaves to be asymptotically stable and periodic (chaotic) at a certain limit order and the other part stabilizes to a fixed point.