The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^sand D^k are given and demonstrated. The method is based on the properties of Euler’s gamma and beta functions.
| Published in | Pure and Applied Mathematics Journal (Volume 2, Issue 1) |
| DOI | 10.11648/j.pamj.20130201.11 |
| Page(s) | 1-9 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2013. Published by Science Publishing Group |
Gamma Functions; Beta Functions; Integrals; Derivatives; Arbitrary Orders; Operators
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APA Style
Raoelina Andriambololona. (2013). Definitions of Real Order Integrals and Derivatives Using Operator Approach. Pure and Applied Mathematics Journal, 2(1), 1-9. https://doi.org/10.11648/j.pamj.20130201.11
ACS Style
Raoelina Andriambololona. Definitions of Real Order Integrals and Derivatives Using Operator Approach. Pure Appl. Math. J. 2013, 2(1), 1-9. doi: 10.11648/j.pamj.20130201.11
AMA Style
Raoelina Andriambololona. Definitions of Real Order Integrals and Derivatives Using Operator Approach. Pure Appl Math J. 2013;2(1):1-9. doi: 10.11648/j.pamj.20130201.11
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Download@article{10.11648/j.pamj.20130201.11,
author = {Raoelina Andriambololona},
title = {Definitions of Real Order Integrals and Derivatives Using Operator Approach},
journal = {Pure and Applied Mathematics Journal},
volume = {2},
number = {1},
pages = {1-9},
doi = {10.11648/j.pamj.20130201.11},
url = {https://doi.org/10.11648/j.pamj.20130201.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.11},
abstract = {The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^sand D^k are given and demonstrated. The method is based on the properties of Euler’s gamma and beta functions.},
year = {2013}
}
TY - JOUR T1 - Definitions of Real Order Integrals and Derivatives Using Operator Approach AU - Raoelina Andriambololona Y1 - 2013/02/20 PY - 2013 N1 - https://doi.org/10.11648/j.pamj.20130201.11 DO - 10.11648/j.pamj.20130201.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 9 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20130201.11 AB - The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^sand D^k are given and demonstrated. The method is based on the properties of Euler’s gamma and beta functions. VL - 2 IS - 1 ER -
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