Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus

Maged Gumaan Bin-Saad

doi:doi:10.11648/j.ml.20160206.12

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Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus

Maged Gumaan Bin-Saad

Published in Mathematics Letters (Volume 2, Issue 6)

Received: 27 August 2016 Accepted: 19 November 2016 Published: 20 December 2016

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Abstract

The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four and several variables are then found. Other closely-related results are also considered.

Published in	Mathematics Letters (Volume 2, Issue 6)
DOI	10.11648/j.ml.20160206.12
Page(s)	47-57
Creative Commons	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.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

N-fractional Calculus Operators, Horn’s Functions, Appell Functions, Saran Functions, Quadruple Functions, Hyper-Geometric of Several Variables

References

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[2]	Maged G. Bin-Saad, Maisoon A. Hussein, Operational images and relations of two and three variable hypergeometric series, Volume 2, Issue 1., J. Prog. Res. Math. (JPRM), 2395-0218.
[3]	Bin-Saad, Maged G., A new multiple hyper-geometric function related to Lauricella’s F⁽ⁿ⁾_A and F⁽ⁿ⁾_D (communicated for publication).
[4]	Chhaya Sharma and C. L. Parihar, Hypergeometric functions of four variables (I), J. Indian Acad. Math. Vol. 11, No.2, (1989), 121-133.
[5]	Chen, M. P., Srivastava, H. M. (1997). Fractional calculus operators and their applications involving power functions and summation of series. Appl. Math. Comput., 81, 283-304.
[6]	Goyal, S. P., Jain, R. M., Gaur, N. (1992). Fractional integral operators involving a product of generalized hypergeometric functions and a general class of polynomials II. Indian J. Pure Appl. Math., 23, 121-128.
[7]	Goyal, S. P., Jain, R. M., Gaur, N. (1991). Fractional integral operators involving a product of generalized hypergeometric functions and a general class of polynomials. Indian J. Pure Appl. Math., 22, 403-411.
[8]	Exton, H., Multiple hypergeometric functions and applications, Ellis Horwood Ltd., Chichester, New York, 1976.
[9]	Exton, H., Hypergeometric functions of three variables, J. Indian Acad. Math. Vol. 4, (1982), 111-119.
[10]	Horn, J., Hypergeometrische Funktionen zweier veranderlichen, Math. Ann. 105, (1931), 381-407.
[11]	Kalla, S. L. (1970). Integral operators of fractional integration. Mat. Notae 22, 89-93.
[12]	Kalla, S. L., Saxena, R. K. (1969). Integral operators involving hypergeometric functions. Math. Zeitschr.108 231-234.
[13]	Kalla, S. L., Saxena, R. K. (1974). Integral operators involving hypergeometric functions II. Univ. Nac. Tucuman Rev. Ser. A 24, 31-36.
[14]	Kant, S., Koul, C. L. (1991). On fractional integral operators. J. Indian Math. Soc. (N. S) 56, 97-107.
[15]	Lauricella, G., Sulle funzioni ipergeometriche a piu variabili. Rend. Circ. Math. Palermo 7, (1898), 111-158.
[16]	Nishimoto, K., Fractional Calculus Vol. I, Descartes Press Co., Koriyuma, Japan, 963(1984).
[17]	Nishimoto, K., Fractional Calculus Vol. II, Descartes Press Co., Koriyuma, Japan, 963 (1984).
[18]	Saran, S., Hypergeometric functions of three variables, Ganita 5, (1954), 77-91.
[19]	Samko, S. G. and A. A. Kilbas, and O. I. Marichev. Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Amsterdam, 1993.
[20]	Sharma, C., Parihar C. L., Hypergeometric functions of four variables (I), Indian Acad. Math. 11 (1989) 121–133.
[21]	Srivastava, H. M. and Karlsson P. W., Multiple Gaussian hypergeometric series, Halsted Press, Bristone, London, New York, 1985.
[22]	Srivastava, H. M. and Manocha, H. L., A treatise on generating functions, Halsted Press, New York, Brisbane and Toronto, 1984.

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Maged Gumaan Bin-Saad. (2016). Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus. Mathematics Letters, 2(6), 47-57. https://doi.org/10.11648/j.ml.20160206.12

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ACS Style

Maged Gumaan Bin-Saad. Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus. Math. Lett. 2016, 2(6), 47-57. doi: 10.11648/j.ml.20160206.12

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AMA Style

Maged Gumaan Bin-Saad. Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus. Math Lett. 2016;2(6):47-57. doi: 10.11648/j.ml.20160206.12

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@article{10.11648/j.ml.20160206.12,
  author = {Maged Gumaan Bin-Saad},
  title = {Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus},
  journal = {Mathematics Letters},
  volume = {2},
  number = {6},
  pages = {47-57},
  doi = {10.11648/j.ml.20160206.12},
  url = {https://doi.org/10.11648/j.ml.20160206.12},
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  abstract = {The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four and several variables are then found. Other closely-related results are also considered.},
 year = {2016}
}

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TY  - JOUR
T1  - Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus
AU  - Maged Gumaan Bin-Saad
Y1  - 2016/12/20
PY  - 2016
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T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
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PB  - Science Publishing Group
SN  - 2575-5056
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AB  - The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four and several variables are then found. Other closely-related results are also considered.
VL  - 2
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Author Information

Maged Gumaan Bin-Saad

Department of Mathematics, Aden University, Aden, Kohrmaksar, Yemen

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APA Style

Maged Gumaan Bin-Saad. (2016). Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus. Mathematics Letters, 2(6), 47-57. https://doi.org/10.11648/j.ml.20160206.12

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ACS Style

Maged Gumaan Bin-Saad. Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus. Math. Lett. 2016, 2(6), 47-57. doi: 10.11648/j.ml.20160206.12

Copy | Download

AMA Style

Maged Gumaan Bin-Saad. Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus. Math Lett. 2016;2(6):47-57. doi: 10.11648/j.ml.20160206.12

Copy | Download

@article{10.11648/j.ml.20160206.12,
  author = {Maged Gumaan Bin-Saad},
  title = {Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus},
  journal = {Mathematics Letters},
  volume = {2},
  number = {6},
  pages = {47-57},
  doi = {10.11648/j.ml.20160206.12},
  url = {https://doi.org/10.11648/j.ml.20160206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160206.12},
  abstract = {The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four and several variables are then found. Other closely-related results are also considered.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Relations Among Certain Generalized Hyper-Geometric Functions Suggested by N-fractional Calculus
AU  - Maged Gumaan Bin-Saad
Y1  - 2016/12/20
PY  - 2016
N1  - https://doi.org/10.11648/j.ml.20160206.12
DO  - 10.11648/j.ml.20160206.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 47
EP  - 57
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20160206.12
AB  - The subject of fractional calculus has gained importance and popularity during the past three decades. Based upon the N-fractional calculus we introduce a new N-fractional operators involving hyper-geometric function. By means of these N-fractional operators a number of operational relations among the hyper-geometric functions of two, three, four and several variables are then found. Other closely-related results are also considered.
VL  - 2
IS  - 6
ER  -

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