On Fractional Newton-Type Method for Nonlinear Problems

Table 1

First-order FNR and second-order FNR results for with Caputo derivative and initial guess .

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	9.65937e − 09	1.23761e − 08	17
N-R	0.98	4.00000000	8.93729e − 09	1.14804e − 08	17
N-R	0.96	3.99999999	6.31251e − 09	2.16859e − 08	28
N-R	0.96	3.99999999	8.36562e − 09	2.82381e − 08	27
N-R	0.94	3.99999997	7.76010e − 09	5.26373e − 08	41
N-R	0.94	3.99999997	8.85140e − 09	5.94304e − 08	40
N-R	0.92	3.99999994	9.40705e − 09	1.13137e − 07	58
N-R	0.92	3.99999995	8.97743e − 09	1.08442e − 07	57
N-R	0.9	3.99999990	9.68422e − 09	1.98513e − 07	82
N-R	0.9	3.99999990	9.48429e − 09	1.94823e − 07	80
N-R	0.88	3.99999984	9.37726e − 09	3.20376e − 07	116
N-R	0.88	3.99999983	9.85311e − 09	3.34523e − 07	112
N-R	0.86	3.99999973	9.78559e − 09	5.41971e − 07	162
N-R	0.86	3.99999973	9.66965e − 09	5.36477e − 07	158
N-R	0.84	3.99999956	9.88726e − 09	8.80428e − 07	227
N-R	0.84	3.99999956	9.82503e − 09	8.75790e − 07	222
N-R	0.82	3.99999930	9.84707e − 09	1.40112e − 06	319
N-R	0.82	3.99999930	9.85142e − 09	1.40163e − 06	313
N-R	0.8	3.99999888	9.90469e − 09	2.23380e − 06	448
N-R	0.8	3.99999888	9.93908e − 09	2.23999e − 06	441
N-R	0.78	3.99999600	2.83959e − 08	8.00875e − 06	500
N-R	0.78	3.99999620	2.65292e − 08	7.59583e − 06	500
N-R	0.76	3.99998275	1.10103e − 07	3.44952e − 05	500
N-R	0.76	3.99998367	1.02423e − 07	3.26542e − 05	500
N-R	0.74	3.99993896	3.53606e − 07	1.22080e − 04	500
N-R	0.74	3.99994240	3.26873e − 07	1.15193e − 04	500
N-R	0.72	3.99981521	9.78747e − 07	3.69503e − 04	500
N-R	0.72	3.99982645	8.96989e − 07	3.47038e − 04	500
N-R	0.7	3.99950671	2.40749e − 06	9.86099e − 04	500
N-R	0.7	3.99953965	2.18121e − 06	9.20282e − 04	500