Operational matrix method approach for fractional partial differential-equations - Turan-Dincel, Arzu; Tural-Polat, Sadiye Nergis (IOP Publishing Ltd, 2024)
Fractional partial differential equations (FPDEs) have become very popular to model and analyze numerous different physical phenomena in recent years. However, it is generally complicated to find the exact solutions of those FPDEs. The objective of this study is to find the approximate numerical solution of FPDEs by introducing a wavelet-based operational matrix technique. In this study we employ Hermite wavelets (HWs) and the operational matrices of the fractional integration for Hermite wavelets. The sparsity of the obtained operational matrices provides fast and efficient computation of the proposed method. The original FPDE equations are converted to Sylvester equations, which then are solved to obtain the final solution. We provide a few numerical examples to demonstrate the versatility and efficiency of the proposed method.
Keywords: hermite wavelets; fractional partial differential equations; sylvester equations; operational matrix; Physics