Chaos in fractional order financial model with fractal–fractional derivatives

Abstract

Recently, a new differential operator which combines fractal differentiation and fractional differentiation with different kernels such as power law, exponential decay, and the Mittag–Leffler function has been introduced. We apply fractal–fractional derivative operators to study chaos in financial chaotic model and implement a numerical procedure to obtain their graphical results. In order to determine the existence of chaos for the chosen value of fractional order, we examine the effects of the saving rate, the per-investment cost, the elasticity of demand, and the Lyapunov exponent. In the case of the classical derivative with power law the obtained attractors presented no similarities. While the attractors obtained via fractal–fractional derivative show some crossover effects. The outcomes of this study are novel and extremely important in dealing with financial issues.