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Titlebook: Erdélyi–Kober Fractional Calculus; From a Statistical P A. M. Mathai,H. J. Haubold Book 2018 The Author(s), under exclusive licence to Spri

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發(fā)表于 2025-3-21 18:31:02 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Erdélyi–Kober Fractional Calculus
副標題From a Statistical P
編輯A. M. Mathai,H. J. Haubold
視頻videohttp://file.papertrans.cn/314/313617/313617.mp4
概述Is the first book to present a statistical perspective for Erdélyi–Kober operators of fractional calculus.Provides the interpretation of the diffusion entropy analysis of solar neutrino data of Super-
叢書名稱SpringerBriefs in Mathematical Physics
圖書封面Titlebook: Erdélyi–Kober Fractional Calculus; From a Statistical P A. M. Mathai,H. J. Haubold Book 2018 The Author(s), under exclusive licence to Spri
描述.This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdélyi–Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics..A major mathematical objective of this book is specifically to examine a new de?nition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a de?nition for the case of real-valued scalar functions of several matrices..
出版日期Book 2018
關(guān)鍵詞Fractional calculus; Fractional operators; Real variable case; Multivariable case; Matrix-variate case
版次1
doihttps://doi.org/10.1007/978-981-13-1159-8
isbn_softcover978-981-13-1158-1
isbn_ebook978-981-13-1159-8Series ISSN 2197-1757 Series E-ISSN 2197-1765
issn_series 2197-1757
copyrightThe Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018
The information of publication is updating

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,Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case,rting the discussion, we will need some Jacobians of matrix transformations here. For results on Jacobians, see Mathai [3]. For the real matrix-variate case, the determinant of . will be denoted by either det(.) or by |.|. When complex matrices are involved we will use the notation det(.) for determ
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發(fā)表于 2025-3-22 12:48:29 | 只看該作者
,Erdélyi-Kober Fractional Integrals Involving Many Real Matrices,for the ratio of .. to .. in the real scalar variable case, ., symmetric ratio, in the real .?×?. matrix-variate case. The corresponding density of .. and .. will be indicated by ..; we will use ..?=?... for the product in the real scalar variable case and ., the symmetric product, in the real .?×?.
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發(fā)表于 2025-3-22 14:26:29 | 只看該作者
,Erdélyi-Kober Fractional Integrals in the Complex Domain,e case. In the present chapter we will look into fractional calculus in the complex domain. Since we will be dealing with .?×?. Hermitian positive definite matrices, for .?=?1 Hermitian positive definite means a real scalar positive variable. Hence we start with .?≥?2. Fractional calculus of one rea
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發(fā)表于 2025-3-23 00:57:56 | 只看該作者
,Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case,be written as ., denoting a matrix . in the complex domain as .. All matrices appearing in this chapter are .?×?. real positive definite unless stated otherwise. Some Jacobians of matrix transformations will be stated here as lemmas without proofs. For proofs and other details, see Mathai [3].
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