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Solving a system of three fractional order differential equations in the sense of Caputo

Hello everyone,
I hope you are in good health.

Here is a system of three fractional order differential equations, I am trying to solve it in the sense of Caputo.
The syntax is correct as it is advised in the documentation but still I cannot get the solution, I do not know what is incorrect.
I need help, it will be highly appreciated.

POSTED BY: Burhanuddin Safi
2 Replies
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Your syntax {t, 0, 12} is typical of NDSolve, not of DSolve. Unfortunately, NDSolve does not support CaputoD at the moment, apparently. DSolve does support it, but in a very limited way: try these two independent equations, that DSolve can solve separately but not together:

eq1 = {CaputoD[S[t], {t, 90/100}] == S[t],
   S[0] == 1};
eq2 = {CaputoD[iI[t], {t, 90/100}] == 3,
   iI[0] == 1};
DSolve[eq1, S[t], t]
DSolve[eq2, iI[t], t]
DSolve[Join[eq1, eq2], {S[t], iI[t]}, t]
POSTED BY: Gianluca Gorni

Thank you very much sir for the guidance. Actually I am trying to know, how an n dimensional system of FDEs in the sense of Caputo derivatives can be solved, unluckily Mathematica is not helpful.
POSTED BY: Burhanuddin Safi
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