Solving Fractional-Order Diffusion Equations in a Plasma and Fluids via a Novel Transform

Table 3

comparison of exact solution, our methods’ solution, and Absolute Error (AE) of Example 4.

	Exact solution	Our methods’ solution	AE of our methods	AE of our methods	AE of our methods
0	0.00000000000000	0.00000000000000	0.000000000E+00	0.000000000E+00	0.000000000E+00
0.1	0.039084756460000	0.039084756470000	8.4147098480E-12	5.8916348320E-06	6.0179783350E-05
0.2	0.077778990960000	0.077778990980000	1.6829419700E-11	1.1724408770E-05	1.1975827680E-04
0.3	0.115696083500000	0.115696083500000	0.0000000000E+00	1.7440075190E-05	1.7814016480E-04
0.4	0.152457179000000	0.152457179000000	0.0000000000E+00	2.2981414070E-05	2.3474221550E-04
0.5	0.187694972800000	0.187694972800000	8.4147098480E-11	2.8293115510E-05	2.8899866580E-04
0.6	0.221057380400000	0.221057380400000	0.0000000000E+00	3.3322251000E-05	3.4036760840E-04
0.7	0.252211055800000	0.252211055900000	8.4147098480E-11	3.8018332270E-05	3.8833574600E-04
0.8	0.280844721700000	0.280844721700000	8.4147098480E-11	4.2334573540E-05	4.3242369270E-04
0.9	0.306672279900000	0.306672280000000	8.4147098480E-11	4.6227807340E-05	4.7219102240E-04
1.0	0.329435670100000	0.329435670200000	8.4147098480E-11	4.9659157730E-05	5.0724039260E-04