in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...

Wansheng Wang School of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China Correspondence should be addressed to Wansheng Wang, [email protected] Received 22 March 2010; Accepted 18 July 2010 Academic Editor: Kun quan Q. Lan Copyright q 2010 Wansheng Wang. This is an open access article distributed under the Creative Commons Attribution L...

This article presents conditions for the oscillation of solutions to neutral partial differential equations. The order of these equations can be even or odd, and the deviating arguments can be distributed over an interval. We also extend our results to a nonlinear equation and to a system of equations.

The paper deals with the oscillation of higher order nonlinear differential equations a neutral term. main results are proved via utilizing an integral criterion as well comparison theorem first-order delay equation whose oscillatory properties known. proposed theorems improve, extend, and simplify existing ones in literature. associated four numerical examples.

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

Sufficient conditions in terms of the coefficient functions for the oscillation and asymptotic behavior of nonoscillatory solutions of a class of second order nonlinear neutral differential equations have been obtained. The results improve some earlier results.

The Banach fixed point theorem and a nonlinear alternative of Leray-Schauder type are used to investigate the existence and uniqueness of solutions for fractional order Hadamard-type functional and neutral functional differential equations.