On Fractional Newton-Type Method for Nonlinear Problems

Table 3

First-order NR and second-order NR results for with Caputo derivative and initial estimation .

N-R	1	−0.00000000	0.00000e + 00	0.00000e + 00	5
N-R	1	−0.00000000	6.66798e − 10	0.00000e + 00	3
N-R	0.98	−0.00000000	2.42649e − 09	1.64532e − 10	8
N-R	0.98	−0.00000000	1.07859e − 09	7.31359e − 11	8
N-R	0.96	−0.00000000	3.91885e − 09	5.46557e − 10	10
N-R	0.96	−0.00000000	2.58893e − 09	3.61075e − 10	10
N-R	0.94	−0.00000000	5.70944e − 09	1.22846e − 09	12
N-R	0.94	−0.00000000	4.32641e − 09	9.30883e − 10	12
N-R	0.92	−0.00000000	2.76674e − 09	8.16363e − 10	15
N-R	0.92	−0.00000000	8.17968e − 09	2.41352e − 09	14
N-R	0.9	−0.00000000	7.94065e − 09	3.01220e − 09	17
N-R	0.9	−0.00000000	6.59632e − 09	2.50224e − 09	17
N-R	0.88	−0.00000000	4.85622e − 09	2.27344e − 09	21
N-R	0.88	−0.00000000	9.82148e − 09	4.59793e − 09	20
N-R	0.86	−0.00000000	7.02051e − 09	3.94299e − 09	25
N-R	0.86	−0.00000000	5.90703e − 09	3.31762e − 09	25
N-R	0.84	−0.00000000	6.69774e − 09	4.42000e − 09	31
N-R	0.84	−0.00000000	9.87756e − 09	6.51845e − 09	30
N-R	0.82	−0.00000001	8.16846e − 09	6.23332e − 09	39
N-R	0.82	−0.00000001	6.60392e − 09	5.03942e − 09	39
N-R	0.8	−0.00000001	7.97894e − 09	6.95120e − 09	52
N-R	0.8	−0.00000001	8.52364e − 09	7.42575e − 09	51
N-R	0.78	−0.00000001	9.79061e − 09	9.63595e − 09	74
N-R	0.78	−0.00000001	8.49008e − 09	8.35597e − 09	73
N-R	0.76	−0.00000001	9.85552e − 09	1.08611e − 08	125
N-R	0.76	−0.00000001	9.15524e − 09	1.00893e − 08	121
N-R	0.74	−0.00000001	9.63986e − 09	1.18037e − 08	360
N-R	0.74	−0.00000001	9.78282e − 09	1.19788e − 08	317
N-R	0.72	−4.31365378	5.71734e − 07	5.23966e − 05	500
N-R	0.72	−0.14393292	1.11043e − 01	1.43663e − 01	500
N-R	0.7	−4.78460364	2.45965e − 01	1.47957e + 00	500
N-R	0.7	−1.29422312	7.32260e − 01	7.50525e − 01	500