Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of th...

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...

The eigenvalues of a matrix A are the zeros of its characteristic polynomial fiX) = dtt[A XI]. With Hyman's method of determinant evaluation, a new homotopy continuation method, homotopy-determinant method, is developed in this paper for finding all eigenvalues of a real upper Hessenberg matrix. In contrast to other homotopy continuation methods, the homotopy-determinant method calculates eigen...