Numerical Investigation of the Fractional Diffusion Wave Equation with the Mittag-Leffler Function

A spline is a sufficiently smooth piecewise curve. B-spline functions are powerful tools for obtaining computational outcomes. They have also been utilized in computer graphics and computer-aided design due to their flexibility, smoothness and accuracy. In this paper, a numerical procedure dependent on the cubic B-spline (CuBS) for the time fractional diffusion wave equation (TFDWE) is proposed. The standard finite difference (FD) approach is utilized to discretize the Atangana-Baleanu fractional derivative (ABFD), while the derivatives in space are approximated through the CuBS with a theta-weighted technique. The stability of the propounded algorithm is analyzed and proved to be unconditionally stable. The convergence analysis is also studied, and it is of the order O(h2+(Delta t)2). Numerical solutions attained by the CuBS scheme support the theoretical solutions. The B-spline technique gives us better results as compared to other numerical techniques.