Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Table 2

Fifth-order approximate numerical solution of equation (20) at different values of the fractional order α and the absolute error E = |u_exact–u_α = 1 | for u (x, y, z, t) by FRDTM.

x	y	z	t	FRDTM for different values of α				uexact	Error (E)
				α = 0.5	α = 0.7	α = 0.9	α = 1
0.1	0.3	0.2	0.3	−1.57206	−1.61233	−1.68227	−1.72641	−1.72641	0
			0.5	−1.47993	−1.43721	−1.41053	−1.41342	−1.41346	4E − 05
		0.8	0.3	−0.97616	−1.00116	−1.04459	−1.072	−1.072	0
			0.5	−0.918948	−0.892426	−0.875856	−0.877649	−0.877679	3E − 05
0.4	0.6	0.2	0.3	−1.02973	−1.05611	−1.10192	−1.13083	−1.13083	0
			0.5	−0.969381	−0.941403	−0.923924	−0.925816	−0.925847	3.1E − 05
		0.8	0.3	−0.43383	−0.444942	−0.464243	−0.476422	−0.476423	1E − 06
			0.5	−0.408403	−0.396616	−0.389252	−0.390049	−0.390062	1.3E − 05
0.7	0.9	0.2	0.3	−0.382167	−0.391956	−0.408958	−0.419687	−0.419687	0
			0.5	−0.359768	−0.349384	−0.342897	−0.3436	−0.343611	1.1E − 05
		0.8	0.3	0.213737	0.219212	0.228721	0.234721	0.234722	1E − 06
			0.5	0.20121	0.195403	0.191775	0.192167	0.192174	7E − 06
1	1	0.2	0.3	0.0939895	0.096397	0.100579	0.103217	0.103217	0
			0.5	0.0884808	0.0859271	0.0843317	0.0845044	0.0845072	2.8E − 06
		0.8	0.3	0.689893	0.707565	0.738258	0.757625	0.757626	1E − 06
			0.5	0.649459	0.630714	0.619004	0.620271	0.620292	2.1E − 05