ON NUMERICAL AND THEORETICAL FINDINGS FOR FRACTAL-FRACTIONAL ORDER GENERALIZED DYNAMICAL SYSTEM

Abstract

In this paper, we consider a general system of fractal-fractional order derivative in Atangana–Baleanu–Caputo sense. On the application of fixed point approach, we establish sufficient conditions regarding existence and uniqueness of solution. The said requirements are obtained via using Krasnoselkii’s and Banach fixed results. Further via nonlinear analysis, some interesting results for Hyers–Ulam (HU)-type stability are also derived. To compute numerical solution for the proposed nonlinear system, fractal-fractional order Adams–Bashforth method is used. To support our findings, we give some test problems. Also by Matlab, we also present their graphical interpretation. The analysis of this paper is in generalized format which can be applied to any real problem. Each equation is investigated separately for the said characteristics.