Fitted spectral tau Jacobi technique for solving certain classes of fractional differential equations

In this paper, an efficient numerical technique, so-called the fitted spectral tau Jacobi (FSTJ), is presented to obtain the solutions of a class of fractional differential equations (FDEs) based on the Jacobi polynomials utilized as natural basis functions under the Caputo sense of fractional derivative. The solution methodology is based on the matrix-vector-product technique in Tau formulation of the model. A comparative study was conducted between the gained results in FSTJ method and other existing methods. Convergence and error analysis are presented to confirm the validity and feasibility of the proposed method for solving such problems. Numerical applications are given which refer to the efficiency and effectiveness of the FSTJ method.