in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

In this article using the inverse Laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. These transfers have been expressed as the Couette flow with the fractional derivative of the Caputo sense. Also, using the Hankel contour for the Bromwich's integral, the solutions are given in terms of the generalized Airy functions.

We evaluate the partition functions in the neighbourhood of catastrophes by saddle point integration and express them in terms of generalized Airy functions.

For a simple Lie algebra g we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of g-type. The dimension of the space of solutions regular at infinity is equal to the rank of the Lie algebra. For the simplest example g = sl2(C) the regular solution can be expressed via products of Airy functions and their derivatives; this matrix valued function...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Bessel and Whittaker func...

The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms, molecules, solids and surfaces show that the Airy gas functional performs better than the local density approximation in all cases and better than the generaliz...