Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

Table 2

Solution of Example 3.1 using 𝛼=0.9, and 𝛼=1.

	𝛼=0.9		𝛼=1.0
𝑥	Appr. solution	Absolute error	Appr. solution	Absolute error
0.0	0.0	0.0	0	0.0
0.1	0.0	4.0000×10^−4	−1.0000×10^−3	6.0000×10^−4
0.2	−2.4593×10^−3	5.9337×10^−5	−2.9700×10^−3	5.7000×10^−4
0.3	−5.4032×10^−3	3.1688×10^−6	−5.6338×10^−3	2.3383×10^−4
0.4	−6.0963×10^−3	3.0367×10^−4	−5.9088×10^−3	4.9117×10^−4
0.5	1.3284×10^−3	1.3284×10^−3	1.5404×10^−3	1.5404×10^−3
0.6	2.5395×10^−2	3.7951×10^−3	2.4489×10^−2	2.8891×10^−3
0.7	7.7426×10^−2	8.8255×10^−3	7.3107×10^−2	4.5075×10^−3
0.8	1.7148×10^−1	1.7883×10^−2	1.5997×10^−1	6.3700×10^−3
0.9	3.2435×10^−1	3.2755×10^−2	3.0005×10^−1	8.4533×10^−3
1.0	5.5552×10^−1	5.5518×10^−2	5.1074×10^−1	1.0736×10^−2