in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

This paper is concerned with a class of continuoustime uncertain systems which satisfy a certain Integral Quadratic Constraint. The problems of robust filtering, robust prediction, and robust smoothing for such systems are defined, and nonconservative solutions are given in terms of Riccati differential equations. This paper also addresses a problem of robust observability for this class of unc...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument αx + βx. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one cubic and one quadratic, possess nontrivial integral solutions whenever the number of variables exceeds 10.

We present an existence theorem for at least one continuous solution for a nonlinear quadratic functional integral equation of fractional (arbitrary) order. Also, we prove the existence of maximal and minimal solutions for that equations. 2000 Mathematics Subject Classification: 32A55; 11D09

As a generalization of the famous four square theorem of Lagrange, Ramanujan and Willerding found all positive definite integral quaternary quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary quadratic forms that represent all positive definite integral binary quadratic forms. We also discuss recent results on positive definite int...