Sentence examples for a generalization of integral from inspiring English sources

Fractional calculus is a generalization of integral and derivative to non-integer order that was first applied by Abel in his study of the tautocrone problem [1].

This fractional Ginzburg-Landau equations can be viewed as a generalization of the integral differential equations proposed by Machida and Koyama (Phys. Rev. A 74 033603, 2006).

For this general operator which is a generalization of more known integral operators we have demonstrated some univalence properties.

Wang (1984 1992) [14] introduced a generalization of the fuzzy integral.

Fractional order differential calculus is only a generalization of integer order integral and differential calculus to real or even complex order.

As a generalization of the fractional integral associated with L, the operators (V^{beta_{2}} -Delta+V)^{-beta_{1} -Delta+Vbeta _{2}leqbeta_{1}leq1), have been studied by Sugano [9] systematically.

The fractional Fourier integral operator is a generalization of the classical Fourier integral operator into the fractional domains.

Fractional calculus is known as a generalization of the derivative and integral of non-integer order.

By introducing some parameters, we establish a generalization of the Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree − 2 λ and the best constant factor which involves the hypergeometric function.

Fractional calculus is as old as the conventional calculus, and it is the generalization of integral order differentiation and integration to arbitrary non-integer order.

The first definition of fractional derivative was introduced at the end of the nineteenth century by Liouville and Riemann, but the concept of non-integer derivative and integral, as a generalization of the traditional integer order differential and integral calculus, was mentioned already in 1695 by Leibniz and L'Hospital.