The Analysis of Fractional-Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform

Table 3

Comparison of the proposed method and exact results with absolute error (AE) at various fractional order for of problem 2.

	Exact solution	Proposed techniques solution	AE of proposed techniques	AE of proposed techniques	AE of proposed techniques
0	−0.333333313300000	−0.333333333300000	2.0000000000E-08	2.0000000000E-08	2.0000000000E-08
0.1	−0.313426424600000	−0.313426443800000	1.9200000000E-08	6.3598200000E-05	6.4898550000E-04
0.2	−0.255343407800000	−0.255343424800000	1.7000000000E-08	1.2227320000E-04	1.2475490000E-03
0.3	−0.163500606900000	−0.163500620500000	1.3600000000E-08	1.7185690000E-04	1.7533551000E-03
0.4	−0.044480856100000	−0.044480865670000	9.5700000000E-09	2.0958106000E-04	2.1381671200E-03
0.5	0.093916578900000	0.093916573300000	5.6000000000E-09	2.3429753000E-04	2.3902801500E-03
0.6	0.243664004500000	0.243664002500000	2.0000000000E-09	2.4637090000E-04	2.5134153000E-03
0.7	0.397340931900000	0.397340933200000	1.3000000000E-09	2.4731770000E-04	2.5230449000E-03
0.8	0.548704820900000	0.548704824600000	3.7000000000E-09	2.3933690000E-04	2.4416045000E-03
0.9	0.692971449700000	0.692971455800000	6.1000000000E-09	2.2486240000E-04	2.2939183000E-03
1.0	0.826845917700000	0.826845923700000	6.0000000000E-09	2.0621260000E-04	2.1036596000E-03