Logistic Fractional Variable-Order Equation - Numerical Simulations for Fitting Parameters

Abstract

The work presents variable-, fractional-order backward difference of the Grünwald-Letnikov type. Variable and fractional-order in the name of the operator means that instead of constant, integer order backward difference, the order of the tested operator is a real value function. The focus is put on presenting the method of finding the parameter of the order function (assuming that the general family of the function is known) and constant $\lambda$ coefficient in a way that values returned by the operator fit some particular simulated data. Mentioned $\lambda$ coefficient is the scaling factor of eigenfunction of the tested backward difference operator.