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 approximate solution obtained by (FHOqTM).

Keywords

• Caputo q-derivative
• Fractional q-difference equations
• Generalized q-Taylor theorem
• Higher-order q-Taylor method