Research Article

Series Solutions of Time-Fractional PDEs by Homotopy Analysis Method

Table 2

Approximate solution of (4.14) for some values of 𝛼 using the 4-term HAM approximation, 𝜙 4 , with = 1 and = 1 . 0 9 6 6 .

𝛼 = 1 . 5 𝛼 = 1 . 7 5 𝛼 = 2 . 0
𝑡 𝑥 = 1 = 1 . 0 9 6 6 = 1 = 1 . 0 9 6 6 = 1 = 1 . 0 9 6 6 Exact

0.20.250.0600490.0601990.0487800.0487880.0434030.0434040.043403
0.500.2401950.2407950.1951190.1951520.1736100.1736170.173611
0.750.5404390.5417890.4390180.4390920.3906230.3906380.390625
1.00.9607810.9631800.7804770.7806070.6944410.6944680.694444

0.40.250.0745360.0769760.0454340.0458210.0318530.0319040.031888
0.500.2981420.3079030.1817360.1832850.1274120.1276160.127551
0.750.6708210.6927830.4089070.4123920.2866770.2871370.286990
1.01.1925701.2316140.7269460.7331410.5096490.5104650.510204

0.60.250.0914690.0997170.0459070.0480480.0239200.0244140.024414
0.500.3658780.3988670.1836260.1921910.0956800.0976560.097656
0.750.8232250.8974500.4131590.4324300.2152800.2197270.219727
1.01.4635111.5954670.7345040.7687650.3827200.3906260.390625