Numerical solution for the time-fractional Fokker–Planck equation via shifted Chebyshev polynomials of the fourth kind

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 The comparative numerical value of the present method with the method [7] for Example 4.1

x	t	α = 0.2		α = 0.4		α = 0.6		α = 0.8		Exact
x	t	TSM	CPFK	TSM	CPFK	TSM	CPFK	TSM	CPFK	Exact
0.2	0.25	1.0254	0.6869	0.8473	0.5540	0.6871	0.4497	0.5542	0.4498	0.45
	0.5	1.1481	0.9380	1.0542	0.8163	0.9384	0.6992	0.8167	0.6996	0.7
	0.75	1.2282	1.1414	1.2046	1.0526	1.1417	0.9495	1.0529	0.9497	0.95
	1	1.2891	1.3185	1.3271	1.2730	1.3192	1.1985	1.2737	1.1993	1.2
0.5	0.25	1.2254	0.8867	1.0473	0.7538	0.8871	0.6493	0.7542	0.6496	0.65
	0.5	1.3481	1.1381	1.2542	1.0164	1.1384	0.8995	1.0167	0.8997	0.9
	0.75	1.4282	1.3417	1.4046	1.2529	1.3417	1.1500	1.2529	1.1500	1.15
	1	1.4891	1.5189	1.5271	1.4734	1.5192	1.3994	1.4737	1.3997	1.4
0.6	0.25	1.4254	1.0863	1.2473	0.9534	1.0871	0.8484	0.9542	0.8492	0.85
	0.5	1.5481	1.3377	1.4542	1.2160	1.3384	1.0987	1.2167	1.0993	1.1
	0.75	1.6282	1.5417	1.6046	1.4529	1.5417	1.3500	1.4529	1.3500	1.35
	1	1.6891	1.7192	1.7271	1.6737	1.7192	1.6000	1.6737	1.6000	1.6