We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schrödinger equation (FSE), characterized by its Lévy index (LI), 1<??2. By means numerical methods, we explore propagation dynamics with vorticities from 0 to 4. The leads abrupt autofocusing, followed reversal (rebound center). It is shown that LI, relative width Airy...

We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by Schrödinger equation (FSE) characterized Lévy index, ?. The autofocusing effect featured such becomes stronger, while focal length shorter, increase intrinsic vorticity on is considered too. Then, ability R-SABs to capture nano-par...

In this paper a higher order non–linear differential equation is given and it becomes a higher order Airy equation (in our terminology) under the Cole–Hopf transformation. For the even case a solution is explicitly constructed, which is a generalization of the Airy function. We start with an example to state our motivation. For the simple non–linear equation of Riccati type y + y = x (1) with a...

In the case of the equidistant discretization of the Airy differential equation (“discrete Airy equation”) the exact solution can be found explicitly. This fact is used to derive a discrete transparent boundary condition (TBC) for a Schrödinger–type equation with linear varying potential, which can be used in “parabolic equation” simulations in (underwater) acoustics and for radar propagation i...

First, this study obtained the fields of an Airy beam (AiB) with optical vortex (OV) for a Fourier transform (FT) system and a fractional Fourier transform (fractional FT) system; thereafter, their intensity and phase patterns were simulated numerically. The splitting on each line of the phase pattern indicates the position of an OV. The results show that the OV position will change when the po...

For a simple Lie algebra g we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of g-type. The dimension of the space of solutions regular at infinity is equal to the rank of the Lie algebra. For the simplest example g = sl2(C) the regular solution can be expressed via products of Airy functions and their derivatives; this matrix valued function...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...