Theory and Modern Applications
Table 1 Time comparison of the approximate solutions of fractional stochastic RC model with external noise for CD, CF, and ABC fractional derivatives at \(\alpha =1\), \(\alpha =0.9\), and \(\alpha =0.8\) and the solution of the Stochastic Runge–Kutta (SRK) method
Time | CD | CF | ABC | SRK | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
α = 1 | α = 0.9 | α = 0.8 | α = 1 | α = 0.9 | α = 0.8 | α = 1 | α = 0.9 | α = 0.8 | ||
10 | 0.999304 | 0.9906497 | 1.050293 | 1.013083 | 1.202816 | 1.0074569 | 1.011102 | 0.806871 | 1.118561 | 1.0121553 |
20 | 1.013781 | 1.0073171 | 1.081426 | 1.059922 | 1.014441 | 1.2262395 | 0.891621 | 0.964927 | 0.963199 | 1.0023026 |
30 | 1.003784 | 0.9606641 | 1.036778 | 0.940042 | 1.095935 | 1.2146484 | 0.941030 | 1.117160 | 0.982169 | 1.0042459 |
40 | 0.973298 | 1.0492959 | 0.938137 | 1.009827 | 0.900094 | 1.5188262 | 0.989640 | 0.749823 | 0.680580 | 1.0014909 |
50 | 1.025356 | 1.0147813 | 0.985297 | 1.028005 | 0.672779 | 1.0174633 | 1.075177 | 1.124972 | 0.856008 | 1.0027986 |
60 | 1.015256 | 1.0591548 | 1.048250 | 0.875409 | 1.266037 | 1.0606401 | 1.080171 | 0.944387 | 1.062668 | 0.9892436 |
70 | 0.918271 | 1.0319845 | 0.937035 | 0.957743 | 0.779292 | 1.0886256 | 1.109512 | 0.948810 | 1.258928 | 1.0041955 |
80 | 0.926106 | 0.9709640 | 0.945952 | 0.975902 | 1.141334 | 0.9260061 | 1.004276 | 1.095910 | 1.062043 | 1.0013826 |
90 | 1.005957 | 1.0632894 | 1.013453 | 1.000967 | 0.674245 | 0.8481464 | 0.971001 | 0.857424 | 1.007927 | 1.0048435 |
100 | 0.906339 | 0.9907657 | 1.015398 | 0.987498 | 0.749267 | 0.9955613 | 1.009571 | 1.219733 | 1.110964 | 1.0009460 |