An efficient analytical approaches to investigate nonlinear two-dimensional time-fractional Rosenau–Hyman equations within the Yang transform

The goal of the current study is to analyze several nonlinear two-dimensional time-fractional Rosenau–Hyman equations. The two-dimensional fractional Rosenau–Hyman equation has extensive use in engineering and applied sciences. The fractional view analysis of two-dimensional time-fractional Rosenau–Hyman equations is discussed using the homotopy perturbation approach, Adomian decomposition method, and Yang transformation. Some examples involving two-dimensional time-fractional Rosenau–Hyman equations are provided to better understand the suggested approaches. The solutions appear as infinite series. We offer a comparison between the accurate solutions and those that are generated employing the proposed approaches to demonstrate the effectiveness and applicability of the proposed techniques. The results are graphically illustrated using two-dimensional and three-dimensional graphs. It has been noted that the obtained results and the targeted problems real solutions are quite similar. Calculated solutions at various fractional levels describe some of the problems useful dynamics. A comparison between the numerical solutions of the models under study and the exact solutions in cases when a solution is known serves as a clear demonstration of the viability and dependability of the suggested approaches. Other fractional problems that arise in other fields of science and engineering can be solved using a modified version of the current techniques.