in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...

Artificially regulating gene expression is an important step in developing new treatment for system-level disease such as cancer. In this paper, we propose a method to regulate gene expression based on sampled-data measurements of gene products concentrations. Inherent noisy behaviour of Gene regulatory networks are modeled with stochastic nonlinear differential equation. To synthesize feed...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of tra...

The paper concerns studies the stochastic stability and stochastic asymptotic stability of the equilibrium solution of a nonlinear Volterra difference equation which is subject to stochastic state independent disturbances. It is shown that if the linearized deterministic equation has summable solutions, then the nonlinear stochastic equation will be stable or asymptotically stable, provided tha...

This article considers the dividend optimization problem for an insurer with a jumpdiffusion risk process in the presence of fixed and proportional transaction costs. Due to the presence of a fixed transaction cost, the mathematical problem becomes an impulse stochastic control problem. Using a stochastic impulse control approach, we transform the stochastic control problem into a quasi-variati...

The Master equation is an infinite dimensional partial differential equation in a state space comprising Euclidean vectors and probability measures. It was introduced by Lasry and Lions for the study of Mean Field Games. We derive this Master Equation from a special Ito formula based on a non-standard differential calculus for functions of probability measures. If time permits, we shall also de...

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlinear differential equations has been described. ...