`CaputoD[f, {x, α}]` gives the Caputo fractional differintegral of `f`. For a
CaputoD[f, {x, α}]
CaputoD[t^2, {t, 1/2}]
→ (8*t^(3/2))/(3*Sqrt[Pi])CaputoD[1, {t, 1/2}]
→ 0CaputoD[t^2, {t, 2}]
→ 2CaputoD[t^2, {t, -1}]
→ t^3/3CaputoD[t^2, {t, alpha}]
→ (2*t^(2 - alpha))/Gamma[3 - alpha]