AN INNOVATIVE NUMERICAL APPROACH FOR TWO-TERM TIME-FRACTIONAL DIFFUSION WAVE EQUATION

This research paper 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.