In this paper we propose a new solution technique for numerical solution of fractional Benney equation, a fourth degree nonlinear fractional partial differential equation with broad range of applications. The method could be described as a hybrid technique which uses advantages of both wavelets and operational matrices. Having applied the present method, fractional Benney equation is converted ...

this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.

The accuracy of the JWKB method for determining the survival factor defined for dissociative electron attachment (DEA) processes is examined for a range of electronic resonance lifetimes within the local complex potential approximation. The author concludes that the accuracy is inadequate for molecules with properties commonly found for shape resonance induced DEA. More accurate methods using t...

In this paper, we answer a question posed by Kurt Johansson, to find a PDE for the joint distribution of the Airy Process. The latter is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion, when the number of particles get large, with space and time appropriately rescaled. The question reduces to an asymptotic analysis on the equation, g...

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

We formulate a fractional stochastic oscillation equation as a generalization of Bagley’s fractional differential equation. We do this in analogous way as in the case of Basset’s equation which gives rise to fractional stochastic relaxation equations. We analyze solutions under some conditions of spatial regularity of the operators considered.

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

in this paper two different methods are presented to approximate the solution of the fractional black-scholes equation for valuation of barrier option. also, the two schemes need less computational work in comparison with the traditional methods. in this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

We have theoretically and numerically investigated the self-healing peculiarity of Airy beams truncated by different decay factors. The self-healing dynamic processes of truncated Airy beams are different from that of blocked Airy beams. The wing with large truncation of Airy beam can propagate much longer distance than that of small truncated wing. When one of the wings is complete truncated, ...

We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the time-independent Schrödinger equation for a quantum particle subjected to a uniform gravitational field. Despite the linear character of the Schrödinger equation, the result we obtain helps in the understanding of the onset of abrupt transitions lea...