Results 11 to 20 of about 1,485,427 (242)
Hypercomplex operator calculus for the fractional Helmholtz equation
Mathematical Methods in the Applied SciencesIn this paper, we develop a hypercomplex operator calculus to treat fully analytically boundary value problems for the homogeneous and inhomogeneous fractional Helmholtz equation where fractional derivatives in the sense of Caputo and Riemann–Liouville are applied.
N Vieira +2 more
exaly +4 more sources
On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order [PDF]
Communications in Contemporary Mathematics, 2022 We show the equivalence of the classical Helmholtz equation and the fractional Helmholtz equation with arbitrary order. This improves a recent result of Guan, Murugan and Wei [Helmholtz solutions for the Fractional Laplacian and other related operators, to appear in Comm. Contemp. Math.].
Cheng, Xinyu, Li, Dong, Yang, Wen
core +6 more sources
مجلة علوم ذي قار, 2019 In this manuscript, we apply a new technique, namely local fractional Laplace variational iteration method (LFVITM) on Helmholtz and coupled Helmholtz equations to obtain the analytical approximate solutions.
Hassan Kamil Jassim +2 more
doaj +7 more sources
Analytical treatment of two-dimensional fractional Helmholtz equations
Journal of King Saud University - Science, 2019 Abstract In this paper, we propose a semi numerical-analytical method, called Fractional Reduced Differential Transform Method (FRDTM), for finding exact and approximate solutions of fractional Helmholtz equation with appropriate initial conditions. The fractional derivatives are demonstrated in the Caputo sense.
Salah Abuasad +2 more
exaly +2 more sources
The method of fundamental solutions for Helmholtz-type problems [PDF]
, 2013 The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated with two- or three-dimensional Helmholtz-type equations.
Bin-Mohsin, Bandar Abdullah
core +6 more sources
The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients [PDF]
, 2012 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least ...
Al-Jawary, Majeed
core +7 more sources
Fractional Solutions for the Helmholtz's Equation in a Multilayered Geometry [PDF]
Progress In Electromagnetics Research, 1999 A generalized fractional order integral operator is derived that relates the one and two dimensional Green's function for a geometry with parallel plane interfaces. It is found that order of the operator is independent of the geometry while lower limit and operational variable are functions of the geometry.
Naqvi, Q. A., Rizvi, A. A.
openaire +2 more sources
Application of Fractional Calculus to Establish Equations of State for Solid Metals
Fractal and Fractional, 2023 Fractional differ-integral operators are used to obtain the equation of state for a substance that can be seen as fractal. Two equations of state have been obtained, the first of which depends on two parameters that characterize the fractal dimension of ...
Vladimir Kulish +2 more
doaj +1 more source
A nonlocal fractional Helmholtz equation [PDF]
Fractional Differential Calculus, 2017 In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered problems are proved by spectral method.
Kirane, Mokhtar +2 more
openaire +2 more sources
Efficient Spectral Collocation Method for Tempered Fractional Differential Equations
Fractal and Fractional, 2023 Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. In this paper, we present a spectral collocation method with tempered fractional Jacobi functions (TFJFs) as basis functions and obtain an efficient algorithm to ...
Tinggang Zhao
doaj +1 more source