Stability of Linear Systems with Caputo Fractional-, Variable-Order Difference Operator of Convolution Type

Abstract

In this article, we investigate asymptotical stability of linear systems with the Caputo fractional-, variable-order difference operator of convolution type. We present the recurrence formula for the solution to linear initial value problems with considered fractional operator. We compare solutions of some examples using numerical calculations in Maple package. We also state and prove necessary conditions for asymptotic stability and instability of considered equations.