The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the meth...

We will consider He’s variational iteration method for solving fractional Riccati differential equation. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converges to the exact solution of the problem. The present method performs extremely well in terms of efficiency ...

Multidimensional integro-differential equations are obtained when the unknown function of several independent variable and/or its derivatives appear under an integral sign. When differentiation or integration operators both fractional order, equation in this case is called a multidimensional equation. Such difficult to solve analytically; therefore, as main objective paper, approximate method—w...

In this paper, a new approach, namely the optimal variational iteration method (OVIM) was proposed to investigate oscillators with fractional-power nonlinearities. It was illustrated that this approach is very effective and convenient and does not require linearization or small parameter. Unlike other classical iteration methods, only one iteration leads to highly accurate results, due to a rig...

This paper has been devoted to apply the Reconstruction of Variational Iteration Method (RVIM) to handle the systems of integro-differential equations. RVIM has been induced with Laplace transform from the variational iteration method (VIM) which was developed from the Inokuti method. Actually, RVIM overcome to shortcoming of VIM method to determine the Lagrange multiplier. So that, RVIM method...

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by min...