Generalizations of the derivative | Linear operators in calculus | Fractional calculus

Differintegral

In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function ƒ, the q-differintegral of f, here denoted by is the fractional derivative (if q > 0) or fractional integral (if q < 0). If q = 0, then the q-th differintegral of a function is the function itself. In the context of fractional integration and differentiation, there are several legitimate definitions of the differintegral. (Wikipedia).

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Related pages

Differential operator | Fractional-order integrator | Function (mathematics) | Fractional calculus | Integral operator | Periodic function | Derivative | Semigroup | Mathematical analysis | Cauchy formula for repeated integration