An approximate solution of fractional cable equation by homotopy analysis method

Boundary Value Problems

Table 2 Comparison of the HPM, HAM, exact solution (ES) and absolute errors results of $u (x, t)$ when $γ_{1} = γ_{2} = 0.5$ , $t = 0.1$ , and $h = - 0.0395$ for 5th-order approximation

x	HPM	HAM	ES	Error (HPM)	Error (HAM)
0.1	−0.340367	0.00309062	0.00309017	0.343458	4.53322 × 10⁻⁷
0.2	−0.647417	0.00587871	0.00587785	0.653295	8.6227 × 10⁻⁷
0.3	−0.891093	0.00809136	0.00809017	0.899184	1.18681 × 10⁻⁶
0.4	−1.04754	0.00951196	0.00951057	1.05705	1.39518 × 10⁻⁶
0.5	−1.10145	0.0100015	0.01	1.11145	1.46698 × 10⁻⁶
0.6	−1.04754	0.00951196	0.00951057	1.05705	1.39518 × 10⁻⁶
0.7	−0.891093	0.00809136	0.00809017	0.899184	1.18681 × 10⁻⁶
0.8	−0.647417	0.00587871	0.00587785	0.653295	8.6227 × 10⁻⁷
0.9	−0.340367	0.00309062	0.00309017	0.343458	4.53322 × 10⁻⁷