This paper is devoted to the study of systems of nonlinear functional differential equations with time-dependent coefficients and multiple variable increasing delays represented by functions gi(t) < t. The solution is found in terms of a piecewise-defined matrix function. Using our representation of the solution and Gronwall’s, Bihari’s and Pinto’s integral inequalities, asymptotic stability re...

We study two-dimensional triangular systems of Newton equations (acceleration = velocity-independent force) admitting three functionally independent quadratic integrals of motion. The main idea is to exploit the fact that the first component M1(q1) of a triangular force depends on one variable only. By using the existence of extra integrals of motion we reduce the problem to solving a simultane...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...

We study a type of third-order linear differential equations with variable and unbounded coefficients, which are defined in an infinite interval. also consider non-linear generalization coefficients that depends on unknown function. establish sufficient conditions for the correctness this equation maximal regularity estimate their solution. Using these results, we prove solvability nonlinear no...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

We discuss new discretization methods for linear differential–algebraic equations with variable coefficients. We introduce numerical methods to compute the local invariants of such differential–algebraic equations that were introduced by the authors in a previous paper. Using these quantitities we are able to determine numerically global invariances like the strangeness index, which generalizes...

Partial differential equations with variable coefficients involving discontinuous case play an important part in engineering, physics and ecology. In this paper, we will study nonlinear partial differential equations with variable coefficients arised from population models. Generally speaking, it is hard to analyze the behavior of nonlinear partial differential equations, therefore we usually r...

The last twenty years has seen considerable and fruitful research in the field of nonsmooth boundary value problems (BVP’s) for partial differential equations. The objective is to understand the behavior and properties of solutions to either variable coefficient equations with minimal regularity assumptions on the coefficients or to linear constant coefficient equations in domains with nonsmoot...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...