Solving Partial Differential Equation with Space- and Time-Fractional Derivatives via Homotopy Decomposition Method

Table 1

Comparison of the numerical results of approximate solutions obtained via HDM, VIM and HPM with exact solution of (27).

Variable 𝑥	HDM	VIM	HPM	Exact	𝐸1 = |HDM−EX|	𝐸2 = |VIM−EX|
1.05	0.78162	0.781619	0.78162	0.781806	0.000186617	0.000187358
1.06	0.785437	0.785426	0.785437	0.785664	0.000226381	0.000237859
1.07	0.789187	0.789179	0.789187	0.789461	0.000274099	0.000282221
1.08	0.792868	0.792789	0.792868	0.793199	0.000331261	0.000410097
1.09	0.796479	0.796467	0.796479	0.796878	0.000399615	0.000411144
1.10	0.800018	0.810017	0.800018	0.800499	0.000481214	0.00951798
1.11	0.803484	0.8100484	0.804062	0.804062	0.000578458	0.00598601

The numerical results show that the HPM and HDM are more accurate than the VIM in this case.