The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as D^(-ν) f(t) = 1/(Γ(ν)) integral_0^t (t - ξ)^(ν - 1) f(ξ) d ξ, where Γ(ν) is the gamma function. From this equation, fractional derivatives can also be defined.

derivative | fractional derivative | fractional differential equation | fractional integral | integral | multiple integral | Riemann-Liouville operator