A New Numerical Approach for Variable-Order Time-Fractional Modified Subdiffusion Equation via Riemann–Liouville Fractional Derivative

Fractional differential equations describe nature adequately because of the symmetry properties that physical and biological processes. In this paper, a new approximation is found for variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on basis, an efficient numerical approach formulated VO time-fractional modified subdiffusion (TFMSDE). Complete theoretical analysis performed, such as stability by Fourier series, consistency, convergence, feasibility proposed also discussed. A example illustrates scheme demonstrates high accuracy, obtained results are more feasible accurate.