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.

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...

Nuclear magnetic resonance (NMR) is a physical phenomenon widely used to study complex materials. NMR is governed by the Bloch equation, a first order non-linear differential equation. Fractional order generalization of the Bloch equation provides an opportunity to extend its use to describe a wider range of experimental situations. Here we present a fractional generalization of the Bloch equat...

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffu...

BACKGROUND Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. RESULTS The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carri...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...