Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

Table 1

Solution of Example 3.1 using 𝛼=0.5 and 𝛼=0.75.

𝑥	𝛼=0.5		𝛼=0.75
	Appr. solution	Absolute error	Appr. solution	Absolute error
0.0	0.0	0.0	0.0	0.0
0.1	0.0	4.0000×10^−4	0.0	4.0000×10^−4
0.2	−3.5668×10^−3	1.1668×10^−3	−2.8054×10^−3	4.0543×10^−4
0.3	−5.6930×10^−3	2.9299×10^−4	−5.8753×10^−3	4.7533×10^−4
0.4	−6.8508×10^−3	4.5080×10^−4	−6.7877×10^−3	3.8767×10^−4
0.5	2.2930×10^−3	2.2930×10^−3	9.7776×10^−4	9.7776×10^−4
0.6	2.8146×10^−2	6.5464×10^−3	2.6460×10^−2	4.8601×10^−3
0.7	8.3911×10^−2	1.5311×10^−2	8.1759×10^−2	1.3159×10^−2
0.8	1.8149×10^−1	2.7885×10^−2	1.8163×10^−1	2.8034×10^−2
0.9	3.3755×10^−1	4.5954×10^−2	3.4348×10^−1	5.1882×10^−2
1.0	5.6863×10^−1	6.8632×10^−2	5.8718×10^−1	8.7178×10^−2