On slowly growing solutions of linear functional differential systems

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

On a Class of Functional Differential Equations Having Slowly Varying Solutions

Functional differential equations with deviating arguments are studied for the first time in the framework of Karamata regularly varying functions. A sharp condition is established for the existence of slowly varying solutions for a class of second order linear equations of the form x′′ = q(t)x(g(t)), both in the retarded and in the advanced case.

Differential transformation method for solving a neutral functional-differential equation with proportional delays

In this article differential transformation method (DTMs) has been used to solve neutral functional-differential equations with proportional delays. The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. Exact solutions can also be obtained from the kno...

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...