The solution to the differential equation [D^(2v) + α D^v + β D^0] y(t) = 0 is y(t) = {e_α(t) - e_β(t) | for α!=β t e^(α t) sum_(k = - (q - 1))^(q - 1) α^k(q - left bracketing bar k right bracketing bar ) D^(1 - (k + 1) v)(t e^(α^q t)) | for α = β!=0 t^(2ν - 1)/(Γ(2v)) | for α = β = 0, auto right match where q | = | 1/v e_β(t) | = | sum_(k = 0)^(q - 1) β^(q - k - 1) E_t(-k v, β^q),

fractional calculus | fractional derivative