Variable-order fractional calculus, chaotic systems, numerical methods, fractional derivatives, nonlinear dynamics

Abstract

    Recently, the V-O-F fractional differential operators have become quite popular for modelling nonlinear dynamical systems with hereditary effects and memory features. However, the V-O-F operator is more suitable for nonlinear dynamical systems with chaotic properties, even though the integer-order derivative operator is a great method for comprehending the behavior of some ordinary differential equations. Here, we present a generalized numerical method to simulate the solution of a broad class of V-O-F differential equations, based on the theorem of fractional calculus and Lagrange interpolation polynomials. The technique may effectively take into account various kernels, including the Atangana-Baleanu-Caputo kernel, the Caputo kernel, and the Caputo-Fabrizio kernel. We use our suggested numerical method to simulate the dynamics of nonlinear chaotic models, specifically a circuit model and a time-varying financial system model.