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On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations

39 Girard St Marlboro, NJ 07746, USA
Mathematics 2020, 8(9), 1418; https://doi.org/10.3390/math8091418
Received: 31 July 2020 / Revised: 18 August 2020 / Accepted: 20 August 2020 / Published: 24 August 2020
(This article belongs to the Special Issue Functional Differential Equations and Applications)
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. View Full-Text
Keywords: fundamental solution; kernel matrix; Borel measures; characteristic matrix; loop-digraph fundamental solution; kernel matrix; Borel measures; characteristic matrix; loop-digraph
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MDPI and ACS Style

McCalla, C. On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations. Mathematics 2020, 8, 1418. https://doi.org/10.3390/math8091418

AMA Style

McCalla C. On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations. Mathematics. 2020; 8(9):1418. https://doi.org/10.3390/math8091418

Chicago/Turabian Style

McCalla, Clement. 2020. "On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations" Mathematics 8, no. 9: 1418. https://doi.org/10.3390/math8091418

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