The Fractional Complex Step Method

Table 1

Equation (7): 𝐷^1/5𝑥²=1.8∗𝑥∗(Δ𝑥)^4/5.

Δ𝑥	Equation (7), 𝑥=0.5	MES (𝑥=0.5)	Equation (7), 𝑥=1	MES (𝑥=1)	Equation (7), 𝑥=1.5	MES (𝑥=1.5)
0.01	0.350714	0.123	1.021427	1.043313	2.282141	5.208166
0.04	0.289158	0.103306	0.898315	0.925142	2.097473	4.803779
0.07	0.24246	0.088466	0.80492	0.832727	1.957381	4.479632
0.1	0.201963	0.076547	0.723927	0.755563	1.83589	4.202347
0.13	0.165237	0.066698	0.650475	0.689074	1.725712	3.957494
0.16	0.131152	0.058449	0.582305	0.630741	1.623457	3.737181
0.19	0.099066	0.051501	0.518131	0.578987	1.527197	3.536488
0.22	0.068567	0.045651	0.457135	0.532735	1.435702	3.352082
0.25	0.039376	0.040751	0.398752	0.491209	1.348128	3.181567
0.28	0.011287	0.036689	0.342574	0.453824	1.263862	3.023145
0.31	−0.01585	0.033376	0.288295	0.420123	1.182442	2.87542
0.34	−0.04216	0.030743	0.235673	0.389741	1.103509	2.737279
0.37	−0.06774	0.028731	0.184518	0.36238	1.026777	2.607817
0.4	−0.09266	0.027292	0.134676	0.337791	0.952013	2.486282
0.43	−0.11699	0.026385	0.086016	0.315765	0.879024	2.372043
0.46	−0.14078	0.025975	0.038432	0.296122	0.807648	2.264558
0.49	−0.16408	0.026031	−0.00817	0.278707	0.737747	2.163365