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Erdélyi–Kober Fractional Calculus

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 31)

DOI: 10.1007/978-981-13-1159-8

ISBN: 978-981-13-1158-1

Publisher: Springer Singapore - Springer Journals

Sep 7, 2018

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Chapter 1Solar Neutrinos, Diffusion, Entropy, Fractional Calculus

Mathai, A. M.; Haubold, H. J.

Pages: 1 –12

[The laws of nature are fundamentally random. This Springer Briefs in Mathematical Physics is an attempt to illustrate elements of a research programme in mathematics and statistics applied to selected problems in physics, particularly the relations between solar neutrinos, diffusion, entropy,...
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Chapter 2Erdélyi-Kober Fractional Integrals in the Real Scalar Variable Case

Mathai, A. M.; Haubold, H. J.

Pages: 13 –42

[This monograph will examine a new definition 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....
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Chapter 3Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case

Mathai, A. M.; Haubold, H. J.

Pages: 43 –72

[General notations on matrices, determinants, traces etc. are given in the introduction to Chap. 2 and hence they will not be repeated here. Before starting the discussion, we will need some Jacobians of matrix transformations here. For results on Jacobians, see Mathai [3]. For the real...
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Chapter 4Erdélyi-Kober Fractional Integrals in the Many Real Scalar Variables Case

Mathai, A. M.; Haubold, H. J.

Pages: 73 –85

[When going from a one-variable function to many-variable function there is no unique one to one correspondence. Many types of multivariate functions can be considered when one has the preselected one-variable function. Hence there is nothing called the multivariate analogue of a univariate...
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Chapter 5Erdélyi-Kober Fractional Integrals Involving Many Real Matrices

Mathai, A. M.; Haubold, H. J.

Pages: 87 –98

[All the matrices appearing in this chapter are p × p real positive definite unless stated otherwise. In order to avoid too many symbols we will use u1=x2x1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
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Chapter 6Erdélyi-Kober Fractional Integrals in the Complex Domain

Mathai, A. M.; Haubold, H. J.

Pages: 99 –119

[In Chaps. 2, 3, 4, and 5 we considered the real scalar variable case, real multivariate case, real one matrix-variate case, real several matrix-variate case. In the present chapter we will look into fractional calculus in the complex domain. Since we will be dealing with p × p Hermitian positive...

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