Results 31 to 40 of about 181,927 (288)

Positive-Definiteness, Integral Equations and Fourier Transforms

Journal of Integral Equations and Applications, 2004
The authors investigate the integral operator \[ A: L^2(\mathbb{R})\to L^2(\mathbb{R}),\quad (Au)(x)= \int^\infty_{-\infty} k(x,y) u(y)\,dy, \] \(x\in\mathbb{R}\), where \(k\) is positive definite kernel function (a special symmetric kernel). Let \(\widehat k(t,s)\) be the Fourier transform of the kernel \(k\) and \(\widetilde k(t,s):=\widehat k(t,-s)\)
Buescu, J., Paixao, A.C., Garcia, F., Lourtie, I.   +3 more
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Transformations between Nonlocal and Local Integrable Equations

Studies in Applied Mathematics, 2017
AbstractRecently, a number of nonlocal integrable equations, such as the ‐symmetric nonlinear Schrödinger (NLS) equation and ‐symmetric Davey–Stewartson equations, were proposed and studied. Here, we show that many of such nonlocal integrable equations can be converted to local integrable equations through simple variable transformations.
Bo Yang, Jianke Yang
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Nonlinear integrable equations and nonlinear Fourier transform [PDF]

, 1997
In the paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Korteweg-de Vries , the nonlinear Schr dinger and the Davey-Stewartson equations.
Fokas, A. S., Gelfand, I. M., Zyskin, M. V.   +2 more
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Abel's Integral Equation as a Convolution Transform [PDF]

Proceedings of the American Mathematical Society, 1956
the first equation to be treated and solved as an integral equation, has an extensive literature, dealing on the one hand with properties of the functions involved, and on the other hand with the solution, and conditions for solubility of the equation. In the first category one might cite, in the modern spirit, the memoirs of Hardy [1, pp.
openaire   +1 more source

Fractional Calculus, Gegenbauer Transformations, and Integral Equations

Journal of Mathematical Analysis and Applications, 1995
This well organized paper starts with discussions of the Weyl and the Riemann-Liouville fractional calculi. A number of identities which connect these fractional integral operators with the Erdélyi-Kober and other operators are developed. The Rodrigues formula for Gegenbauer polynomials is then generalized to an integral relation for Gegenbauer ...
van Berkel, C.A.M., Eijndhoven, van, S.J.L.   +1 more
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On a New Integral Transform and Differential Equations [PDF]

Mathematical Problems in Engineering, 2010
Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering.
Kilicman, Adem, Eltayeb, Hassan
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A note on dual integral equations involving inverse associated Weber-Orr transforms

International Journal of Mathematics and Mathematical Sciences, 1996
We consider dual integral equations involving inverse associated Weber-Orr transforms. Elementary methods have been used to reduce dual integral equations to a Fredholm integral equation of second kind. Some known results are obtained as special case.
Nanigopal Mandal, B. N. Mandal
doaj   +1 more source

Applications of Mohand Transform

Journal of Innovative Science and Engineering
Investigating solutions of differential equations has been an important issue for scientists. Researchers around the world have talked about different methods to solve differential equations.
Nihal ÖZDOĞAN
doaj   +1 more source

Solving Partial Differential Equations Using the New Integral Transform “Double SEE Integral Transform”

Journal of Physics: Conference Series, 2022
Abstract The immense importance of differential equations and integral transforms in scientific fields leads to inducting the integral transforms as a solving tool for partial differential equations. The “double SEE integral transform” is a novel integral transform suggested in this research.
Emad A Kuffi, Eman A Mansour
openaire   +1 more source

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

, 2017
We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian.
AA Golovin, AH Stroud, Alexandre Ern, BJ West, IG Graham, IH Sloan, IH Sloan, Krzysztof Bogdan, L Caffarelli, LR Scott, M D’Elia, Mark Ainsworth, Mark Ainsworth, MG Duffy, MM Meerschaert, P Ciarlet, Raffaella Servadei, RH Nochetto, RK Getoor, S Erichsen, SA Silling, Stefan A. Sauter, T Koto, W Hackbusch, WCH McLean, Y Yan, ZQ Chen   +26 more
core   +1 more source