General Theory Of Linear Systems Research Articles

On a Method of Solution of Systems of Fractional Pseudo-Differential Equations.

This paper is devoted to the general theory of linear systems of fractional order pseudo-differential equations. Single fractional order differential and pseudo-differential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudo-differential equations is still far from completeness, even in the linear case. In this paper we develop a new method of solution of general systems of fractional order linear pseudo-differential equations and prove existence and uniqueness theorems in the special classes of distributions, as well as in the Sobolev spaces.

The Theory of Linear Continuous Systems. I†

ABSTRACT In this paper a general theory of linear systems is outlined In which the systems are treated as operators satisfying certain simple continuity conditions. The main object is to show the oxtent to which a rigorous account of the subject depends on the theory of Lebesgue-Stieltjes integration and to develop the necessary apparatus for the integration theory in a natural manner. The explicit representation of linear operators in terms of convolution integrals, together with the formal definition of integration itself, is to be undertaken in the second part of the paper. The first part gives a detailed discussion of the fundamental properties of linearity and continuity attributed to physical systems. The presentation adopted makes available all the mathematical equipment necessary for the subsequent account of integration theory.