Elzaki residual power series approach for semi-analytic approximation of time-fractional nonlinear equations occurring in magneto-acoustic waves

Abstract The study of magneto-sound propagation in plasma, capillary gravity water waves, and the travel of long waves under the effect of gravity in shallow water are all important applications of the 5th-order Korteweg–de Vries equation. This research article uses the Elzaki residual power series method(ERPSM), an appropriate innovative technique, to explore time-fractional nonlinear 5th-order Korteweg–de Vries equations. Three instances of the time-fractional 5th-order Korteweg–de Vries equations in order to demonstrate the effectiveness and relevance of the proposed method has been examined. This work's originality is expressed by an analysis of the fractional behavior of the considered equations.There is a discernible difference in the solutions that are produced for various fractional orders, which may have distinct ramifications for further work. Readers can employ the hybrid approaches combining with our proposed scheme as a future study direction to get better results. Additionally, appropriate numerical simulations were setup to confirm the accuracy and dependability of the suggested strategy. The results collected indicate that the suggested approach is highly satisfying and looks at the intricate nonlinear problems that occur in innovation and science.