Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Abstract The accurate numerical solution of partial differential equations (PDEs) is a central task in analysis allowing to model wide range natural phenomena by employing specialized solvers depending on the scenario application. Here, we develop variational approach for solving PDEs governing evolution high dimensional probability distributions. Our naturally works unbounded continuous domain...

in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a q-Gaussian trial wave-function that interpolates between the low-and the high-density limit of the ground state of a Bose-condensed gas. Our main result consists of reducing the Gross-Pitaevskii equation, a nonlinear partial ...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent Newton methods for nonsmooth equations have been well established via the concept of semismoothness. When the constraint set of the variational inequality problem is a rectangle, several locally convergent Newton methods for the reformulated nonsmooth e...

We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the Lagrangian framework by treating the action as a Volterra series. It is then possible to derive two equations of motion, one of these is an advanced equation and ...