Numerical evaluation with the fractional Newton explicit group technique for a certain class of fractional partial differential equations

The present paper gives an accurate technique for solving Caputo’s fractional Burger equations and fractional Fisher equations using the fractional Newton explicit group method. In this technique, the fractional derivative operator in the interval (0, 1) is approximated by an implicit finite difference scheme (FDM). Numerical simulations of the two models under study are presented by comparing the results for various values of the order of the fractional derivatives to estimate the accuracy and efficiency of the given technique for solving these two problems. The method is applied to the proposed equations to demonstrate the consistency of its achievement in solving such systems. Also, a comparison with the solutions of another technique for distinct quantities of the size of the matrices introduced in the same method, the calculation of the error, and the time taken are presented, through which we can confirm that the proposed method outperforms or complements the existing techniques. Finally, from the proposed numerical results, we can confirm the effectiveness of this technique in solving such real phenomena.