We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n–dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time–dependent Hamilton– Jacobi equation of the mechanics so defined.

In this article, the (G ′ /G)-expansion method has been implemented to find the travelling wave solutions of nonlinear evolution equations of fractional order. For this, the fractional complex transformation method has been used to convert fractional order partial differential equation to ordinary differential equation. Then, (G ′ /G)-expansion method has been implemented to celebrate the serie...

The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the ...

In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with t...

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

A fast approximate inversion method is proposed for the block lower triangular Toeplitz with tri-diagonal blocks (BL3TB) matrix. The BL3TB matrix is approximated by a block ε-circulant matrix, which can be efficiently inverted using the fast Fourier transforms. The error estimation is given to show the high accuracy of the approximation. In applications, the proposed method is employed to solve...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is ...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...