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

‎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.