Related papers: Applications of integral transforms in fractional …
By using similarity transformations approach, the exact propagator for a generalized one-dimensional Fokker-Planck equation, with linear drift force and space-time dependent diffusion coefficient, is obtained. The method is simple and…
We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Existence and uniqueness of advanced and retarded fundamental solutions (Green's functions) and of global solutions to the Cauchy problem is proved for a general class of first order linear differential operators on vector bundles over…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical…
Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
In this paper we study generalized time-fractional diffusion equations on the Poincar\`e half plane $\mathbb{H}_2^+$. The time-fractional operators here considered are fractional derivatives of a function with respect to another function,…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
In this note, I would like to discuss an approach to the construction of Green's function on algebraic surfaces, indicated by Manin, towards the computation of the Green's function on surfaces using Schottky uniformization. We shall see…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…
This paper is devoted to the analysis of some fundamental problems of linear elasticity in 1D continua with self-similar interparticle interactions. We introduce a self-similar continuous field approach where the self-similarity is…
This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo…
An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…