On Fractional Newton-Type Method for Nonlinear Problems

Table 2

First-order FNR and second-order FNR results for with Riemann–Liouville derivative and initial estimation .

N-R	1	4.00000000	1.46549e − 14	2.84217e − 14	10
N-R	1	4.00000000	8.38330e − 18	0.00000e + 00	8
N-R	0.98	4.00000000	4.68492e − 09	4.77773e − 09	16
N-R	0.98	4.00000000	6.74956e − 09	6.72255e − 09	15
N-R	0.96	3.99999999	9.31417e − 09	2.26436e − 08	20
N-R	0.96	3.99999999	6.15820e − 09	1.54268e − 08	21
N-R	0.94	3.99999999	8.41656e − 09	3.90606e − 08	28
N-R	0.94	3.99999998	9.57249e − 09	4.39009e − 08	28
N-R	0.92	3.99999997	9.83530e − 09	7.65395e − 08	35
N-R	0.92	3.99999997	8.10233e − 09	6.42359e − 08	38
N-R	0.9	3.99999994	9.40993e − 09	1.18506e − 07	49
N-R	0.9	3.99999994	9.37709e − 09	1.18142e − 07	47
N-R	0.88	3.99999991	9.61954e − 09	1.88983e − 07	65
N-R	0.88	3.99999990	9.84849e − 09	1.92880e − 07	64
N-R	0.86	3.99999986	9.60193e − 09	2.89676e − 07	86
N-R	0.86	3.99999985	9.96806e − 09	2.99047e − 07	85
N-R	0.84	3.99999978	9.53412e − 09	4.36870e − 07	114
N-R	0.84	3.99999978	9.64049e − 09	4.40927e − 07	113
N-R	0.82	3.99999966	9.94288e − 09	6.80455e − 07	150
N-R	0.82	3.99999966	9.91663e − 09	6.78992e − 07	149
N-R	0.8	3.99999949	9.98970e − 09	1.02156e − 06	199
N-R	0.8	3.99999950	9.78692e − 09	1.00502e − 06	199
N-R	0.78	3.99999924	9.96299e − 09	1.51847e − 06	265
N-R	0.78	3.99999924	9.98659e − 09	1.52126e − 06	264
N-R	0.76	3.99999888	9.90426e − 09	2.24483e − 06	354
N-R	0.76	3.99999887	9.98421e − 09	2.25855e − 06	353
N-R	0.74	3.99999833	9.92379e − 09	3.33049e − 06	473
N-R	0.74	3.99999833	9.94614e − 09	3.33603e − 06	473
N-R	0.72	3.99999551	2.29296e − 08	8.98833e − 06	500
N-R	0.72	3.99999548	2.30961e − 08	9.03519e − 06	500
N-R	0.7	3.99998762	5.73722e − 08	2.47620e − 05	500
N-R	0.7	3.99998750	5.81547e − 08	2.49976e − 05	500