On systems of linear differential equations having regular singular solutions

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...

Formal series solutions of singular systems of linear differential equations and singular matrix pencils

A system of n linear differential equations xy'{x) =x~8B{x)y(x) is considered, in which s is a positive integer and B(x) is a formal power series. In a preceding paper [6] the author has developed a method for evaluating a formal fundamental matrix solution to the system. This method leads to the algebraic treatment of certain singular matrix pencils. In the present paper the author provides so...

On Regular and Logarithmic Solutions of Ordinary Linear Differential Systems

On Periodic Solutions of Systems of Linear Functional Differential Equations

This paper deals with the system of functional-diierential equations dx(t) dt = p(x)(t) + q(t); where p : C!(R n) ! L!(R n) is a linear bounded operator, q 2 L!(R n), ! > 0 and C!(R n) and L!(R n) are spaces of n-dimensional !-periodic vector functions with continuous and integrable on 0;!] components, respectively. Conditions which guarantee the existence of a unique !-periodic solution and co...

On Bounded Solutions of Systems of Linear Functional Differential Equations

Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established. 1. Formulations of the Main Results Let R be the set of real numbers, Cloc(R, R) be the space of continuous functions u : R → R with the topology of uniform convergence on every compact interval and Lloc(R,R) be the space of locally summ...