a numerical method for solving distributed order time fractional covid-19 virus model based on legendre wavelets optimization approach

In this paper, we introduced a distributed order time fractional coronavirus-19 disease transmission involving caputo-prabhakar fractional derivative of α order in time t. the coronavirus 19 disease model has 8 inger dients leading to system of 8 nonlinear ordinary differential equations in this sense. to solve these types of equations, we proposed a numerical method based on the upon legendre wavelets optimization approximations. in the first stage, by applying the legendre wavelets optimization functions and laplace transform an exact formula for the prabhakar fractional integral operator is derived. then, we apply this exact formula and the properties of legendre wavelets optimization functions to change the given equation into a system of algebraic equations. we calculated the approximation optimal solutions of our system applying the newton's iterative method. the optimal approximate solutions obtained by using the proposed method are considered as the best solutions for the proposed equation. error analysis is examined to verify the practical efficiency of the proposed method. in the end, for the efficiency and performance of the proposed method, the numerical results are shown in the figure.