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.

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governi...

this paper is concerned with investigation of vertical impedance function of a surface rigid circular foundation resting on a semi-infinite transversely isotropic alluvium. to this end, the equations of motion in cylindrical coordinate system, which because of axissymmetry are two coupled equations, are converted into one partial differential equation using a method of potential function. the g...

commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...

A study is presented of the axially symmetric deformation of a non-homogeneous elastic halfspace subjected to torsional shear tractions that are linearly distributed over a circular portion of the otherwise free surface. The problem is formulated in terms of Hankel integral transforms and an inverse procedure is implemented in which the determination of the type of non-homogeneity constitutes p...

In this note we explore the properties of a simply defined family of Riordan arrays [9]. The inverses of these arrays are closely related to well-known Catalan-defined matrices. This motivates us to study the Hankel transforms [6] of the images of some well-known families of sequences under the inverse matrices. This follows a general principle which states that the Hankel transform of the imag...

The non-linear transformations for accelerating the convergence of slowly convergent infinite integrals due to Levin & Sidi (1975) are modified in two ways. These modifications enable one to eval uate accurately some oscillatory infinite integrals with less work. Special emphasis is placed on the evaluation of Fourier and Hankel transforms and some simple algorithms for them are given. Converge...