On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations
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 t...
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doaj-524364e2573340cfb43cf14703846dab2020-11-25T03:43:34ZengMDPI AGMathematics2227-73902020-08-0181418141810.3390/math8091418On Fundamental Solution for Autonomous Linear Retarded Functional Differential EquationsClement McCalla039 Girard St Marlboro, NJ 07746, USAThis 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 the 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 an 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.https://www.mdpi.com/2227-7390/8/9/1418fundamental solutionkernel matrixBorel measurescharacteristic matrixloop-digraph |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Clement McCalla |
spellingShingle |
Clement McCalla On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations Mathematics fundamental solution kernel matrix Borel measures characteristic matrix loop-digraph |
author_facet |
Clement McCalla |
author_sort |
Clement McCalla |
title |
On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations |
title_short |
On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations |
title_full |
On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations |
title_fullStr |
On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations |
title_full_unstemmed |
On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations |
title_sort |
on fundamental solution for autonomous linear retarded functional differential equations |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-08-01 |
description |
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 the 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 an 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. |
topic |
fundamental solution kernel matrix Borel measures characteristic matrix loop-digraph |
url |
https://www.mdpi.com/2227-7390/8/9/1418 |
work_keys_str_mv |
AT clementmccalla onfundamentalsolutionforautonomouslinearretardedfunctionaldifferentialequations |
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1724518980716068864 |