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]