The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients

In this paper, a numerical method based on the third kind Chebyshev wavelets is proposed for solving a class of time-fractional convection diffusion equations with variable coefficients. The third kind Chebyshev wavelets operational matrices of the integer order integration and the fractional order integration are derived respectively. They are utilized to reduce the problem to a system of linear algebraic equations by combining the collocation method. The uniform convergence analysis and error estimation for the third kind Chebyshev wavelets expansion are investigated. Illustrative examples are given and the numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.