We discuss and derive the analytical solution for three basic problems of the so-called timefractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in...

From a suitable integral representation of the Laplace transform of a positive semi–definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furth...

We give some precisions on the Fourier-Laplace transform theorem for tempered ultrahyperfunctions introduced by Sebastião e Silva and Hasumi, by considering the theorem in its simplest form: the equivalence between support properties of a distribution in a closed convex cone and the holomorphy of its Fourier-Laplace transform in a suitable tube with conical basis. We establish a generalization ...

A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Lapl...

other areas. However, the spectral properties of the Laplace transform tend to complicate its numerical treatment; therefore, the closely related “truncated” Laplace transforms are often used in applications. In this dissertation, we construct efficient algorithms for the evaluation of the singular value decomposition (SVD) of such operators. The approach of this dissertation is somewhat simila...

other areas. However, the spectral properties of the Laplace transform tend to complicate its numerical treatment; therefore, the closely related “truncated” Laplace transforms are often used in applications. In this dissertation, we construct efficient algorithms for the evaluation of the singular value decomposition (SVD) of such operators. The approach of this dissertation is somewhat simila...

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...

In this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body fo...

In this paper, four types of fractional Fourier cosine and sine Laplace weighted convolutions are defined, the corresponding convolution theorems associated with transform, transform derived in detail. Furthermore, relationship between (sine) existing studied, Young's type theorem is also investigated. addition, as an application for (sine)-Laplace convolution, system convolution-type integral ...

This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf’s) and probability mass functions (pmf’s) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines. The Fourier-series method can be interprete...