Solitary Wave Solutions for a Time-Fraction Generalized Hirota-Satsuma Coupled KdV Equation by a New Analytical Technique

Table 1

Numerical values when 𝛼=0.5, 0.75, 1.0 and 𝑘=0.1, 𝛽=1.5, 𝑐₀=1.5, 𝑐₁=0.1 for 𝑢(𝑥,𝑡).

𝑡	𝑥	𝛼=0.5		𝛼=0.75		𝛼=1.0
		𝑢FIM	𝑢HPM	𝑢FIM	𝑢HPM	𝑢FIM	𝑢HPM	𝑢Exact
0.2	0	0.4935113355	0.4933513333	0.4933937249	0.4933513333	0.4933513226	0.4933513333	0.4933513225
	0.25	0.4935979177	0.4934136490	0.4934546200	0.4934060408	0.4933937118	0.4933937581	0.4933937115
	0.5	0.4937081918	0.4935005536	0.4935399023	0.4934853752	0.4934607890	0.4934608711	0.4934607891
	0.75	0.4938416235	0.4936116158	0.4936491516	0.4935889426	0.4935522228	0.4935523392	0.4935522227
	1	0.4939975728	0.4937462882	0.4937818335	0.4937162326	0.4936675611	0.4936677111	0.4936675613
0.4	0	0.4936853330	0.4934053333	0.4935033001	0.4934053333	0.4934051602	0.4934053333	0.4934051609
	0.25	0.4938008948	0.4935090262	0.4935963610	0.4934954686	0.4934771397	0.4934775983	0.4934771401
	0.5	0.4939391903	0.4936368323	0.4937131147	0.4936097847	0.4935733947	0.4935741334	0.4935733945
	0.75	0.4940995646	0.4937881198	0.4938529939	0.4937477171	0.4936934501	0.4936944620	0.4936934499
	1	0.4942812668	0.4939621476	0.4940153259	0.4939085897	0.4938367205	0.4938379949	0.4938367203
0.6	0	0.4938553137	0.4934953333	0.4936435681	0.4934953333	0.4934944586	0.4934953333	0.4934944625
	0.25	0.4939921388	0.4936348749	0.4937639292	0.4936174202	0.4935955155	0.4935973485	0.4935955186
	0.5	0.4941508292	0.4937979026	0.4939071763	0.4937630802	0.4937202663	0.4937230371	0.4937202675
	0.75	0.4943306471	0.4939836133	0.4940726248	0.4939315968	0.4938681006	0.4938717813	0.4938681010
	1	0.4945307679	0.4941911034	0.4942594934	0.4941221502	0.4940383061	0.4940428589	0.4940383061