Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method

Table 1

The approximate solution of fractional Rosenau-Hynam equation using fifth iterates of VIM and fifth terms of HPM in different values of 𝛼, that is, 𝛼=0.7,0.8, and 0.9 and 𝛼=1.0 when 𝑐=0.5.

𝑥	𝑡	VIM	HPM	VIM	HPM	VIM	HPM	VIM	HPM	Exact
		𝛼=0.7		𝛼=0.8		𝛼=0.9		𝛼=1.0
𝜋/4	0.2	−1.3027037	−1.3020263	−1.2995666	−1.2994063	−1.2968978	−1.2968865	−1.1139217	−1.2945674	−1.2945674
	0.6	−1.3163161	−1.3160219	−1.3159022	−1.3158706	−1.3150924	−1.3150940	−1.3137953	−1.3137952	−1.3137952
	1.0	−1.3194666	−1.3204884	−1.3228476	−1.3231121	−1.3251352	−1.3251648	−1.3265574	−1.3265572	−1.3265572
𝜋/2	0.2	−1.1781765	−1.1775095	−1.1715349	−1.1713677	−1.1658775	−1.1658583	1.1610425	−1.1610425	−1.1610425
	0.6	−1.2168471	−1.2161259	−1.2124978	−1.2123777	−1.2080227	−1.2079404	−1.2032236	−1.2032236	−1.2032236
	1.0	−1.2404292	−1.2410937	−1.2415934	−1.2417625	−1.2413894	−1.2412100	−1.2400439	−1.2400437	−1.2400437
3𝜋/4	0.2	−0.4677769	−0.9752216	−0.4579952	−0.9664930	−0.4496547	−1.1658655	−0.4426464	−0.2194117	−0.4426464
	0.6	−0.5359648	−1.0325797	−0.5255989	−1.0258054	−0.5158600	−1.0185228	−0.5064510	−0.2710013	−0.5064510
	1.0	−0.5899819	−1.0742478	−0.5848618	−1.0728597	−0.5788060	−1.0701462	−0.5718564	−0.3265443	−0.5718565
𝜋	0.2	−0.7263173	−0.7259589	−0.7160797	−0.7159725	−0.7073528	−0.7073345	−0.6999861	−0.6999861	−0.6999861
	0.6	−0.7945239	−0.7933266	−0.7847888	−0.7845575	−0.7754812	−0.7753489	−0.7662921	−0.7662921	−0.7662921
	1.0	−0.8456349	−0.8453513	−0.8421984	−0.8421178	−0.8374790	−0.8371566	−0.8316027	−0.8316026	−0.8316026