ANALYSIS AND COMPACT DIFFERENCE APPROXIMATION FOR FRACTIONAL-ORDER REACTION–DIFFUSION EQUATION WITH A NON-SINGULAR KERNEL: LAPLACE TRANSFORMATION

This work offers an approximation for the 1D temporal fractional order reaction–diffusion equation (FRDE). The fractional order (FO) temporal derivative is approximated implicitly using the Laplace transformation (LT), followed by numerical discretization, as well as the space derivative; a higher-order approximation is utilized. The LT reduced the fractional order derivative (FOD) to an integer order, providing a numerical solution for the resulting numerical difference scheme. Theoretical analyses, including stability, consistency, and convergence, are discussed using the Fourier series method. The mathematical trial is performed to justify the proficiency of the new approximated technique.