Preprint Article Version 1 This version is not peer-reviewed

On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations

Version 1 : Received: 24 July 2020 / Approved: 26 July 2020 / Online: 26 July 2020 (03:00:42 CEST)

How to cite: McCalla, C. On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations. Preprints 2020, 2020070632 (doi: 10.20944/preprints202007.0632.v1). McCalla, C. On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations. Preprints 2020, 2020070632 (doi: 10.20944/preprints202007.0632.v1).

Abstract

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix, and the Laplace transform. The fundamental solution is presented in a form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of a RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

Subject Areas

fundamental solution; functional differential equation; kernel matrix; Borel measures; characteristic matrix; loop-digraph

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