A Parameter Switching Algorithm for Fractional-Order Systems

This paper adapts the parameter switching algorithm to a class of fractional-order systems modeled with the Caputo derivative. The algorithm, originally designed for integer-order autonomous systems that depend linearly on a real parameter, involves switching the parameter during numerical integration according to a predefined rule. The resulting attractor approximates a target attractor corresponding to an average of the switched parameters. The convergence of the method is proven analytically and demonstrated numerically on the fractional Lorenz system and a fractional dark matter and dark energy system.