A Novel Numerical Approach for Handling Fractional Quantum Initial-Value Problems

In this study, we propose a novel version of the fractional q-trapezoid formula, which is used to solve fractional initial-value problems. This is achieved by utilizing the so-called fractional q−Taylor expansion, particularly the fractional q-forward and q-backward Euler formulas. To ensure the robustness of the proposed method, a stability analysis is conducted to explore its performance under various conditions and demonstrate its reliability. Furthermore, various numerical examples are provided to validate the findings, accuracy, and efficacy, thus demonstrating the potential of this method for tackling complicated fractional problems.