Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 6 Numerical comparison of RK solutions of Example 5.3

From: An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

Caputo–Fabrizio derivative
t	α = 0.95	α = 0.9	α = 0.85	α = 0.8
0.1	0.878154	0.841424	0.809596	0.779507
0.2	0.803522	0.775775	0.754698	0.735620
0.3	0.734319	0.715288	0.702245	0.689792
0.4	0.670852	0.659133	0.652587	0.646019
0.5	0.612250	0.606508	0.604833	0.602217
0.6	0.558018	0.556914	0.558814	0.559845
0.7	0.507762	0.510076	0.514403	0.515875
0.8	0.461224	0.465891	0.471920	0.485746
0.9	0.418228	0.424361	0.430753	0.345449
1.0	0.378651	0.385541	0.396784	0.307297

Caputo derivative
t	α = 0.95	α = 0.9	α = 0.85	α = 0.8
0.1	0.890657	0.877026	0.861834	0.845039
0.2	0.798776	0.782397	0.765453	0.748147
0.3	0.719922	0.704886	0.690238	0.676195
0.4	0.651426	0.639660	0.628876	0.619175
0.5	0.591366	0.583572	0.576929	0.571390
0.6	0.538143	0.534214	0.531258	0.529125
0.7	0.490422	0.489770	0.489718	0.490092
0.8	0.447148	0.448978	0.450998	0.453077
0.9	0.407549	0.411063	0.414430	0.417593
1.0	0.371111	0.375624	0.379777	0.383579

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