$New explicit formulas for the some special matrices with fractional derivatives: II$

New explicit formulas for the some special matrices with fractional derivatives: II

Matrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α is the order of fractional derivative, were obtained. The defin...

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Main Authors:	Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng
Format:	Article
Language:	English
Published:	Elsevier 2021-06-01
Series:	Ain Shams Engineering Journal
Subjects:	Matrix exponential Explicit formulas Caputo fractional derivative Riemann-Liouville fractional derivative
Online Access:	http://www.sciencedirect.com/science/article/pii/S2090447920302318

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spelling	doaj-656d47eb18a7460d8b797769e41aac7e2021-06-07T06:47:07ZengElsevierAin Shams Engineering Journal2090-44792021-06-0112220832088New explicit formulas for the some special matrices with fractional derivatives: IIJian-Gen Liu0Xiao-Jun Yang1Yi-Ying Feng2School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China; State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR ChinaSchool of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China; State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China; School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China; Corresponding author.State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China; School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR ChinaMatrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α is the order of fractional derivative, were obtained. The definitions of the fractional derivative respectively are the Caputo fractional derivative and Riemann-Liouville fractional derivative. Here, we need to point that the new results can be looked as an extended the previous work of the authors. The explicit formulas can help us better to explore deep connotations from natural science.http://www.sciencedirect.com/science/article/pii/S2090447920302318Matrix exponentialExplicit formulasCaputo fractional derivativeRiemann-Liouville fractional derivative
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jian-Gen Liu Xiao-Jun Yang Yi-Ying Feng
spellingShingle	Jian-Gen Liu Xiao-Jun Yang Yi-Ying Feng New explicit formulas for the some special matrices with fractional derivatives: II Ain Shams Engineering Journal Matrix exponential Explicit formulas Caputo fractional derivative Riemann-Liouville fractional derivative
author_facet	Jian-Gen Liu Xiao-Jun Yang Yi-Ying Feng
author_sort	Jian-Gen Liu
title	New explicit formulas for the some special matrices with fractional derivatives: II
title_short	New explicit formulas for the some special matrices with fractional derivatives: II
title_full	New explicit formulas for the some special matrices with fractional derivatives: II
title_fullStr	New explicit formulas for the some special matrices with fractional derivatives: II
title_full_unstemmed	New explicit formulas for the some special matrices with fractional derivatives: II
title_sort	new explicit formulas for the some special matrices with fractional derivatives: ii
publisher	Elsevier
series	Ain Shams Engineering Journal
issn	2090-4479
publishDate	2021-06-01
description	Matrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α is the order of fractional derivative, were obtained. The definitions of the fractional derivative respectively are the Caputo fractional derivative and Riemann-Liouville fractional derivative. Here, we need to point that the new results can be looked as an extended the previous work of the authors. The explicit formulas can help us better to explore deep connotations from natural science.
topic	Matrix exponential Explicit formulas Caputo fractional derivative Riemann-Liouville fractional derivative
url	http://www.sciencedirect.com/science/article/pii/S2090447920302318
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_version_	1721392745615982592

New explicit formulas for the some special matrices with fractional derivatives: II

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