Abstract
This paper aims to develop an improved Hermite wavelet resolution method for solving space–time-fractional partial differential equations (STFPDE). Unlike the previous wavelet methods in which operational matrices are constructed by using orthogonal functions and block pulse functions, we have directly formulated the Riemann–Liouville fractional integral (RLFI) operator for Hermite wavelets of general order integration. We have also shown the error bounds of the established method to demonstrate the theoretical applicability of the proposed method. The accuracy of the developed method is tested via a descriptive comparison of the numerical results with those obtained from other existing methods. The investigative results validate that the introduced technique is stable, authentic, straightforward, and computationally reliable.
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