Numerical study on time-fractional convection-diffusion equation

In this research‎, ‎ a method to numerically solve a time-fractional convection-diffusion equation‎ is presented that is based upon the operational matrices of shifted Jacobi polynomials‎. ‎Problem is converted to a homogeneous problem by interpolation and afterwards 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 which is solved by MathematicaTM‎. ‎In order to indicate the high efficiency method we implement the proposed method for several examples.