Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method

Table 1

Approximate solution of (4.1) for some values of 𝛼 using the 4-term HAM approximation, 𝜙₄, with ℏ=−1 and ℏ=−1.0453.

𝑡	𝑥	𝛼=1.5		𝛼=1.75		𝛼=2.0
		ℏ=−1	ℏ=−1.045	ℏ=−1	ℏ=−1.045	ℏ=−1	ℏ=−1.045	Exact
0.2	0.25	0.26284062	0.26284062	0.26266989	0.26266991	0.26258350	0.26258350	0.26258350
	0.50	0.55136246	0.55136250	0.55067959	0.55067964	0.55033400	0.55033402	0.55033400
	0.75	0.86556554	0.86556562	0.86402909	0.86402919	0.86325150	0.86325156	0.86325150
	1.0	1.20544985	1.20544999	1.20271839	1.20271856	1.20133600	1.20133610	1.20133600
0.4	0.25	0.27697114	0.27697109	0.27615668	0.27615669	0.27567202	0.27567205	0.27567202
	0.50	0.60788455	0.60788437	0.60462675	0.60462679	0.60268808	0.60268820	0.60268808
	0.75	0.99274025	0.99273983	0.98541019	0.98541027	0.98104818	0.98104846	0.98104818
	1.0	1.43153821	1.43153748	1.41850702	1.41850715	1.41075232	1.41075282	1.41075232
0.6	0.25	0.29309481	0.29309501	0.29109009	0.29108997	0.28979084	0.28979084	0.28979084
	0.50	0.67237924	0.67238006	0.66436039	0.66435990	0.65916338	0.65916339	0.65916339
	0.75	1.13785328	1.13785513	1.11981088	1.11980978	1.10811762	1.10811764	1.10811764
	1.0	1.68951694	1.68952024	1.65744156	1.65743961	1.63665355	1.63665358	1.63665358