نتایج جستجو برای: fractional airy equation

تعداد نتایج: 284107  

1995
Kenji Kajiwara Yasuhiro Ohta Junkichi Satsuma

We present a class of solutions to the discrete Painlevé-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the τ function for the discrete PII and the that of the discrete Toda molecule equation is pointed out.

Journal: :The Journal of the Acoustical Society of America 2008
James F Kelly Robert J McGough Mark M Meerschaert

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation ["Time domain wave-equations for lossy media obeying a frequency power-law," J. Ac...

ژورنال: پژوهش های ریاضی 2015
Arab Ameri , M., Mir Mehrabi , E,

Fractional derivatives and integrals are new concepts of derivatives and integrals of arbitrary order. Partial differential equations whose derivatives can be of fractional order are called fractional partial differential equations (FPDEs). Recently, these equations have received special attention due to their high practical applications. In this paper, we survey a rather general case of FPDE t...

Journal: :iranian journal of oil & gas science and technology 2014
maryam ghorbani mohammad reza khorsand mohsen masihi

the performance of water flooding can be investigated by using either detail numerical modeling or simulation, or simply through the analytical buckley-leverett (bl) model. the buckley-leverett analytical technique can be applied to one-dimensional homogeneous systems. in this paper, the impact of heterogeneity on water flooding performance and fractional flow curve is investigated. first, a ba...

2003
ENRICO SCALAS

The fractional diffusion equation is derived from the master equation of continuous time random walks (CTRWs) via a straightforward application of the GnedenkoKolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.

2008
Vasily E. Tarasov George M. Zaslavsky

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

Journal: :Symmetry 2022

The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework fractional Schrödinger equation, which includes saturable or cubic self-focusing defocusing nonlinearity and Lévy index ((LI) alias for fractionality) taking values 1≤α≤2. model applies to light a chain optical cavities emulating diffraction. Management included by making diffraction and/or coefficients...

Journal: :Optics letters 2014
Pedro Chamorro-Posada Julio Sánchez-Curto Alejandro B Aceves Graham S McDonald

We present a numerical study of the giant Goos-Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence ...

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