mohsen khasteh

In this paper, we proposed a numerical method based on the shifted fractional order Jacobi and trapezoid methods to solve a type of distributed partial differential equations. The fractional derivatives are considered in the Caputo-Prabhakar type. By shifted fractional-order Jacobi polynomials our proposed method can provide highly accurate approximate solutions by reducing the problem under study to a set of algebraic equations which is technically simpler to handle. In order to demonstrate the error estimates, several lemmas are provided. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis.

In this paper, we proposed a numerical approach to solve a distributed order time fractional COVID 19 virus model. The fractional derivatives are shown in the Caputo-Prabhakar contains generalized Mittag-Leffler Kernel. The coronavirus 19 disease model has 8 Inger diets leading to system of 8 nonlinear ordinary differential equations in this sense, we used the midpoint quadrature method and finite different scheme for solving this problem, our approximation method reduce the distributed order time fractional COVID 19 virus equations to a system of algebraic equations. Finally, to confirm the efficiency and accuracy of this method, we presented some numerical experiments for several values of distributed order. Also, all parameters introduced in the given model are positive parameters.