A New Fractional Approach for the Higher-Order q-Taylor Method
DOI:
https://doi.org/10.5566/ias.3286Keywords:
Caputo q-derivative, Fractional q-difference equations, Generalized q-Taylor theorem, Higher-order q-Taylor methodAbstract
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).
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Copyright (c) 2024 Nadia Allouch, Iqbal M. Batiha, Iqbal H. Jebril, Samira Hamani, Areen Al-Khateeb, Shaher Momani
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