Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

Table 2

HPTM for the approximate solution of Example 1.

	at	at	at	Exact solution
(0.1, 0.1)	−0.0939215	−0.0939015	−0.09389	−0.09389
(0.1, 0.3)	−0.0939536	−0.0939319	−0.0939146	−0.0939146
(0.1, 0.5)	−0.0939757	−0.0939571	−0.0939391	−0.0939391
(0.2, 0.1)	−0.0915064	−0.091487	−0.0914759	−0.0914759
(0.2, 0.3)	−0.0915375	−0.0915165	−0.0914997	−0.0914997
(0.2, 0.5)	−0.0915589	−0.0915409	−0.0915235	−0.0915235
(0.3, 0.1)	−0.0891657	−0.0891469	−0.0891361	−0.0891361
(0.3, 0.3)	−0.0891958	−0.0891754	−0.0891592	−0.0891592
(0.3, 0.5)	−0.0892166	−0.0891992	−0.0891822	−0.0891822
(0.4, 0.1)	−0.0868965	−0.0868782	−0.0868678	−0.0868678
(0.4, 0.3)	−0.0869257	−0.0869059	−0.0868901	−0.08688901
(0.4, 0.5)	−0.0869458	−0.0869289	−0.0869125	−0.0869125
(0.5, 0.1)	−0.0846961	−0.0846784	−0.0846683	−0.0846683
(0.5, 0.3)	−0.0847244	−0.0847052	−0.0846899	−0.0846899
(0.5, 0.5)	−0.0847439	−0.0847275	−0.0847116	−0.0847116