The modified homotopy perturbation method for solving strongly nonlinear oscillators

In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Padé approximants. This modified homotopy perturbation method (MHPM) utilizes an alternative framework to capture the periodic behavior of the solution, which is characteristic of oscillator equations, and to give a good approximation to the true solution in a very large region. The current results are compared with those derived from the established Runge–Kutta method in order to verify the accuracy of the MHPM. It is shown that there is excellent agreement between the two sets of results. Results also show that the numerical scheme is very effective and convenient for solving strongly nonlinear oscillators

Derivation of a new Merton's optimal problem presented by fractional stochastic stock price and its applications

In this article, a new model of Merton's optimal problem is derived. This derivation is based on stock price presented by fractional order stochastic differential equation. An extension of Hamilton-Jacobi-Bellman is used to transfer our proposed model to a fractional partial differential equation. As an application of our proposed model, two optimal problems are discussed and solved, analytically.This publication was made possible by NPRP grant NPRP 5-088-1-021 from the Qatar National Research Fund (a member of Qatar Foundation).Scopu