On Fractional Newton-Type Method for Nonlinear Problems

Table 4

First-order NR and second-order NR results for with Riemann–Liouville 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	9.29969e − 10	5.95854e − 11	8
N-R	0.96	−0.00000000	3.91885e − 09	5.46557e − 10	10
N-R	0.96	−0.00000000	2.40538e − 09	3.14007e − 10	10
N-R	0.94	−0.00000000	5.70944e − 09	1.22846e − 09	12
N-R	0.94	−0.00000000	4.82173e − 09	9.60702e − 10	12
N-R	0.92	−0.00000000	2.76674e − 09	8.16363e − 10	15
N-R	0.92	−0.00000000	3.43115e − 09	9.26171e − 10	15
N-R	0.9	−0.00000000	7.94065e − 09	3.01220e − 09	17
N-R	0.9	−0.00000000	5.89937e − 09	2.01913e − 09	18
N-R	0.88	−0.00000000	4.85622e − 09	2.27344e − 09	21
N-R	0.88	−0.00000000	4.71244e − 09	1.95934e − 09	23
N-R	0.86	−0.00000000	7.02051e − 09	3.94299e − 09	25
N-R	0.86	−0.00000000	5.93748e − 09	2.90861e − 09	30
N-R	0.84	−0.00000000	6.69774e − 09	4.42000e − 09	31
N-R	0.84	−0.00000000	7.64084e − 09	4.30750e − 09	43
N-R	0.82	−0.00000001	8.16846e − 09	6.23332e − 09	39
N-R	0.82	−0.00000001	8.48988e − 09	5.40319e − 09	79
N-R	0.8	−0.00000001	7.97894e − 09	6.95120e − 09	52
N-R	0.8	−0.00506018	1.02936e − 02	7.19943e − 03	500
N-R	0.78	−0.00000001	9.79061e − 09	9.63595e − 09	74
N-R	0.78	−0.07024016	1.47568e − 01	9.83535e − 02	500
N-R	0.76	−0.00000001	9.85552e − 09	1.08611e − 08	125
N-R	0.76	−0.14147226	2.83238e − 01	1.86505e − 01	500
N-R	0.74	−0.00000001	9.63986e − 09	1.18037e − 08	360
N-R	0.74	−1.57171790	2.40309e + 00	1.13046e + 00	500
N-R	0.72	−4.31365378	5.71734e − 07	5.23966e − 05	500
N-R	0.72	−0.00000000	9.36668e − 09	5.10297e − 09	157
N-R	0.7	−4.78460364	2.45965e − 01	1.47957e + 00	500
N-R	0.7	0.00000000	9.82670e − 09	5.30280e − 09	101
N-R	0.68	−5.71070798	5.01626e − 01	1.03562e + 01	500
N-R	0.68	0.00000000	8.29674e − 09	4.54705e − 09	85
N-R	0.66	−754.27892554	7.80349e + 01	2.58569e + 18	500
N-R	0.66	−0.00000000	8.34916e − 09	4.76503e 09	82
N-R	0.64	−1411860.53657482	1.42625e + 05	3.96270e + 44	500
N-R	0.64	0.00000000	9.54192e − 09	5.80404e − 09	89
N-R	0.62	−1063648380.57639720	1.04707e + 08	4.10943e + 67	500
N-R	0.62	−0.00000000	8.55254e − 09	5.65282e − 09	113
N-R	0.6	−875382037053.40283000	8.39601e + 10	8.59364e + 90	500
N-R	0.6	−3.22839026	2.60655e − 07	1.73936e − 04	500