A New Fractional Approach for the Higher-Order q-Taylor Method

Abstract

The main goal of this work is to propose a new fractional approach of the higher order q-Taylor method with Initial Value Problems (IVPs) for fractional q-difference equations which is called the Fractional Higher-Order q-Taylor Method (FHOqTM). By applying the generalised q-Taylor theorem, this would be achieved. As a consequence, we calculate the FHOqTM’s local truncation error. Finally, we present numerical applications to validate our results by comparing the exact solution and the approximatesolution resulting from (FHOqTM).