On the sulutions of a fractional differemtial equation

We have showed the results obtained in [1] are incorrect and the fractional complex transform is invalid to the fractional differential equation which contain modified Riemann-Liouville fractional derivative

HPM for Solving the Time-fractional Coupled Burgers Equations

In this paper, the homotopy perturbation method is implemented to derive the explicit approximate solutions for the time-fractional coupled Burger's equations. The including fractional derivative is in the Caputo sense. Special attention is given to prove the convergence of the method. The results are compared with those obtained by the exact at special cases of the fractional derivatives. The results reveal that the proposed method is very effective and simple

A Convenient Adomian-Pade Technique for the Nonlinear Oscillator Equation

Very recently, the convenient way to calculate the Adomian series was suggested. This paper combines this technique and the Pade approximation to develop some new iteration schemes. Then, the combined method is applied to nonlinear models and the residual functions illustrate the accuracies and conveniences

Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the Lagrangian of the regular KdV equation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that leads to the time fractional KdV equation. The Riemann-Liouvulle definition of the fractional derivative is used to describe the time fractional operator in the fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations of the solution with initial condition A0*sech(cx)^2 are carried out. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone. The effects of the time fractional parameter on the electrostatic solitary structures are presented.Comment: 1 tex file + 5 eps figure

Application of homotopy-perturbation method to fractional IVPs

Fractional initial-value problems (fIVPs) arise from many fields of physics and play a very important role in various branches of science and engineering. Finding accurate and efficient methods for solving fIVPs has become an active research undertaking. In this paper, both linear and nonlinear fIVPs are considered. Exact and/or approximate analytical solutions of the fIVPs are obtained by the analytic homotopy-perturbation method (HPM). The results of applying this procedure to the studied cases show the high accuracy, simplicity and efficiency of the approach

Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method

The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. Very recently, a novel way was proposed by Duan (2010) to calculate the Adomian series which is a crucial step of the Adomian decomposition method. In this paper, it was used to solve some fractional nonlinear differential equations

Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation

Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the economic and financial fields. Laplace decomposition method is one of the reliable and effective numerical methods for solving fractional differential equations. Thus, this paper aims to apply the Laplace decomposition method for solving the fractional Black-Scholes equation, where the fractional derivative used is the Caputo sense. Two numerical illustrations are presented in this paper. The results show that the Laplace decomposition method is an efficient, easy and very useful method for finding solutions of fractional Black-Scholes partial differential equations and boundary conditions for European option pricing problems

Solving Time-Fractional Korteureg-de

In this paper, an analytic solution which has to do with the series expansion approach is proposed to determine the solution of time K-de V equation, specifically by FRDTM. The fractional derivatives are demonstrated in the Caputo sense. We compare the obtained results with R-K fourth order Method. It is possible to obtain solution closed to exact solution of a partial differential equation. To sum it up all, the accuracy, robustness, efficiency and convergence of this techniques are then illustrated through the numerical examples presented in this paper