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

Table 2

The approximate solution of fractional Rosenau-Hynam using fifth iterate 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=1.0.

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	−2.6345127	−2.6293263	−2.6251671	−2.6239643	−2.6172579	−2.6171710	−2.6099581	−2.6099581	−2.6099581
	0.6	−2.6345745	−2.6342711	−2.6474590	−2.6477297	−2.6563851	−2.6450822	−2.6609433	−2.6609420	−2.6609420
	1.0	−2.5722042	−2.5854045	−2.6080979	−2.6122085	−2.6365766	−2.6372049	−2.6590258	−2.6589984	−2.6589984
𝜋/2	0.2	−2.4277172	−2.4226797	−2.4036916	−2.4024670	−2.3832715	−2.4054513	−2.3655561	−2.3655561	−2.3655561
	0.6	−2.5350335	−2.5308256	−2.5303337	−2.5295597	−2.5232013	−2.5409052	−2.5126533	−2.5126523	−2.5126523
	1.0	−2.5563768	−2.5641211	−2.5831444	−2.5854712	−2.6015950	−2.6030469	−2.6127547	−2.6127328	−2.6127328
3𝜋/4	0.2	−0.5752642	−2.0501900	−0.5416828	−2.0182039	−0.5130518	−1.9893536	−0.4893583	−0.4893583	−1.9640076
	0.6	−0.8341872	−2.5308256	−0.7891721	−2.2292752	−0.7486279	−2.1055837	−0.7112517	−0.7112526	−2.1848220
	1.0	−1.0486958	−2.3554614	−1.0195238	−2.3681073	−0.9896491	−2.3733581	−0.9579284	−0.9579473	−2.3716903
𝜋	0.2	−1.5711438	−2.4226797	−1.5304096	−1.5296754	−1.4957251	−1.5301673	−1.4664446	−1.4664446	−1.4664446
	0.6	−1.8301141	−2.5308256	−1.7949603	−1.7925916	−1.7612479	−1.7971174	−1.7273603	−1.7273603	−1.7273603
	1.0	−1.9968865	−2.5641211	−1.9951864	−1.9932084	−1.9871083	−2.0042754	−1.9725695	−1.9725674	−1.9725674