An Innovative Numerical Approach for Two-Term Time-Fractional Diffusion Wave Equation

This research article mainly focuses on two things: modeling the time-fractional diffusion wave equation and developing a new discretization for the Riemann-Liouville fractional derivative operator. The Riemann-Liouville fractional derivative is discretized for both first- and second-order derivatives, then used for the temporal derivative discretization of fractional order Formula: see text, and the spatial derivative is discretized by a compact Crank-Nicolson difference scheme. The Von-Neumann analysis method is used to compute the stability and convergence of theoretical analysis. Numerical analysis involves errors, tables, and graphical computation, validating the theoretical results.