Application of Local Fractional Homotopy Perturbation Method in Physical Problems

Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of u(x,t) with alpha = 1 and 0.33, t = 0.1 sec, between the present research and Yong-Ju Yang study for x >= 0.6 is less than 10. Also, the % error for x >= 0.5 in alpha = 1 and 0.33, t = 0.3 sec, is less than 5, whereas for alpha = 1 and 0.33, t = 0.8 and 0.7 sec, the % error for x >= 0.4 is less than 8.