A New Fractional Approach for the Higher-Order q-Taylor Method - Allouch, Nadia; Batiha, Iqbal M.; Jebril, Iqbal H.; Hamani, Samira; Al-Khateeb, Areen; Momani, Shaher (Image Analysis and Stereology, 2024)
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).