An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation

• Operational matrix of shifted Jacobi polynomials is considered.
• Solution of time-fractional order convection–diffusion problem is numerically estimated.
• Main problem is converted to a homogeneous problem by interpolation and afterward an integro-differential equation is yielded.
• A system of nonlinear algebraic equations is achieved by approximating the known and unknown functions with the help of shifted Jacobi functions.
• Problem can be used extensively in science and engineering as in oil reservoir simulations.

In this article, we present a numerical method to numerically solve a time-fractional convection–diffusion equation. Our method is based on the operational matrices of shifted Jacobi polynomials. At first, problem is converted to a homogeneous problem by interpolation and afterward an integro-differential equation is yielded. Then we approximate the known and unknown functions with the help of shifted Jacobi functions. A system of nonlinear algebraic equations is obtained. Finally, the unknown coefficients are determined by MathematicaTM. We implemented the proposed method for several examples that they indicate the high accuracy method. It should be noted that this method is generalizable to some appropriate problems.