In this paper we establish some new exact solutions regarding to the unsteady flow of a generalized Oldroyd-B fluid produced by a suddenly moved plate between two side walls perpendicular to the plate. The governing equation has been obtained through fractional calculus approach. Fourier sine transform and discrete Laplace transform have been used to obtained exact solutions. The solution of ve...

In a series of papers, we discussed the solution of Laplace’s differential equation (DE) by using fractional calculus, operational calculus in the framework of distribution theory, and Laplace transform. The solutions of Kummer’s DE, which are expressed by the confluent hypergeometric functions, are obtained with the aid of the analytic continuation (AC) of Riemann–Liouville fractional derivati...

In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf’s (e.g.,...

Abstract In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf...

Abstract. The Fourier slice theorem used for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with using algorithms for unequally spaced fast Laplace transforms to construct fast and accurate methods for computing, both the forward exponential Radon transform and the corresponding back...

— For a regular twistor D-module and for a given function f , we compare the nearby cycles at f =∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier-Laplace transform relative to the kernel e−τf .

Engineers and students in communications and mathematics are confronted with transformations such as the z-Transform, the Fourier transform, or the Laplace transform. Often it is quite hard to quickly find the appropriate transform in a book or the Internet, much less to have a comprehensive overview of transformation pairs and corresponding properties. In this document I compiled a handy colle...

A one-dimensionalmodel of an in vitro experiment, inwhich a specimen of cancellous bone is immersed in water and insonified by an ultrasonic pulse, is considered. Themodification of the poroelastic model of Biot due to Johnson et al. [D.L. Johnson, J. Koplik, R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech. 176 (1987) 379–402] is used for ...

A method is described for inverting the Laplace transform. The performance of the Fourier method is illustrated by the inversion of the test functions available in the literature. Results are shown in the tables.