Pell Wavelet Optimization Method for Solving Time-Fractional Convection Diffusion Equations Arising in Science and Medicine

چکیده مقاله

Here, we present a composition method for solving time-fractional convection-diffusion equations (TF-CDEs). The main aims of the technique are to use Pell wavelets and convert the considered problem into fractional partial integro-differential equations, utilizing the Riemann-Liouville fractional integration (RL). For this approach, we consider Pell wavelets as an efficient tool to develop the method. We compute the RL pseudo-operational matrix for these functions. Taking RL for the considered problem and using the properties of RL, with the help of a pseudo-operational matrix and optimization scheme, we present the framework of the suggested scheme. Moreover, for approximate results, we evaluate the upper bound of errors. As a result, we apply the method by solving some numerical samples. Our approximate results illustrate that the computational scheme is powerful and applicable to solve the mentioned problems, and we can implement this to solve different kinds of fractional problems. © 2024 University of Kashan Press. All rights reserved.