An approximate solution of fractional cable equation by homotopy analysis method

Boundary Value Problems

Table 4 Comparison of the HPM, HAM, exact solution (ES) and absolute errors results of $u (x, t)$ when $γ_{1} = 0.25$ , $γ_{2} = 0.75$ , $t = 0.1$ , and $h = - 0.0043$ for 10th-order approximation

x	HPM	HAM	ES	Error (HPM)	Error (HAM)
0.1	−5022.62	0.00305436	0.00309017	5022.62	3.58117 × 10⁻⁵
0.2	−9553.59	0.00580973	0.00587785	9553.6	6.8118 × 10⁻⁵
0.3	−13149.4	0.00799641	0.00809017	13149.4	9.37564 × 10⁻⁵
0.4	−15458.0	0.00940035	0.00951057	15458.0	1.10217 × 10⁻⁴
0.5	−16253.5	0.00988411	0.01	16253.6	1.15889 × 10⁻⁴
0.6	−15458.0	0.00940035	0.00951057	15458.0	1.10217 × 10⁻⁴
0.7	−13149.4	0.00799641	0.00809017	13149.4	9.37564 × 10⁻⁵
0.8	−9553.59	0.00580973	0.00587785	9553.6	6.8118 × 10⁻⁵
0.9	−5022.62	0.00305436	0.00309017	5022.62	3.58117 × 10⁻⁵