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2013 | 11 | 10 | 1314-1336
Article title

Riemann-Liouville and Caputo type multiple Erdélyi-Kober operators

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Abstracts
EN
In this paper some generalized operators of Fractional Calculus (FC) are investigated that are useful in modeling various phenomena and systems in the natural and human sciences, including physics, engineering, chemistry, control theory, etc., by means of fractional order (FO) differential equations. We start, as a background, with an overview of the Riemann-Liouville and Caputo derivatives and the Erdélyi-Kober operators. Then the multiple Erdélyi-Kober fractional integrals and derivatives of R-L type of multi-order (δ
1,…,δ
m) are introduced as their generalizations. Further, we define and investigate in detail the Caputotype multiple Erdélyi-Kober derivatives. Several examples and both known and new applications of the FC operators introduced in this paper are discussed. In particular, the hyper-Bessel differential operators of arbitrary order m > 1 are shown as their cases of integer multi-order. The role of the so-called special functions of FC is emphasized both as kernel-functions and solutions of related FO differential equations.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1314-1336
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
Contributors
  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, “Acad. G. Bontchev” Str., Block 8, 1113, Sofia, Bulgaria, virginia@diogenes.bg
author
  • Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences, Luxemburger Str. 10, D - 13353, Berlin, Germany, luchko@beuth-hochschule.de
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0217-1
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