in this paper, differential transform method (dtm) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in hiv infections of cell. intervals of validity of the solution will be extended by using pade approximation. the results also will be compared with those results obtained by runge-kutta method. the technique is described and is illustrat...

Two systems of fractional order functional and neutral functional differential equations with infinite delay are studied in this article, and some sufficient conditions for existence of unique solutions for these two systems are established by Banach fixed point theorem.

We study point and higher symmetries for the hydrodynamic-type systems with two independent variables t and x with and without explicit dependence of the equations on t, x. We consider those systems which possess an infinite group of the hy-drodynamic symmetries, establish existence conditions for this property and, using it, derive linearizing transformations for these systems. The recursion o...

Despite long history of research and rich literature devoted to optimization problems, relatively few works concerning optimal control for infinite dimensional systems can be found. Moreover, they mostly present approaches suitable for PDE models. This paper is concerned with optimal control problem for certain class of infinite dimensional systems as well as some dynamical properties of such s...

In this paper, we are interested in solving infinite linear systems of differential equations of the form x′ (t) = Tx (t) + b with x(0) = x0, where T is either the generalized Cesàro operator C (λ) or the weighted mean matrix Nq, x0 and b are two given infinite column matrices and λ is a sequence with non-zero entries. We use a new method based on Laplace transformations to solve these systems.

Abstract This paper is concerned with the asymptotic analysis of infinite systems weakly coupled stationary Hamilton–Jacobi–Bellman equations as discount factor tends to zero. With a specific Hamiltonian, we show convergence solution and prove solvability corresponding ergodic problem.

in this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. first, by a replacement, we transform thesystem to the sturm-liouville equation with a turning point. using the asymptotic estimates for a specialfundamental system of solutions of sturm-liouville equation, we study the infinite product rep...