Explore: Fractional Integrals

numerous contributors have given different definitions for fractional derivatives and integrals. Let f ( x ) {\displaystyle f(x)} be a function defined for

setting negative values for a yields integrals. For a general function f(x) and 0 < α < 1, the complete fractional derivative is D α f ( x ) = 1 Γ ( 1

particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study

D q f {\displaystyle \mathbb {D} ^{q}f} is the fractional derivative (if q > 0) or fractional integral (if q < 0). If q = 0, then the q-th differintegral

into a single integral (cf. Cauchy's formula). For non-integer n it yields the definition of fractional integrals and (with n < 0) fractional derivatives

stochastic integrals with respect to fractional Brownian motion, usually called "fractional stochastic integrals". In general though, unlike integrals with

Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. Using

physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study

A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative

The Katugampola fractional integral generalizes both the Riemann–Liouville fractional integral and the Hadamard fractional integral into a single form