# Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly; Sebastian, Nicy

Fractional Calculus and Applied Analysis (2010)

- Volume: 13, Issue: 2, page 159-176
- ISSN: 1311-0454

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topKilbas, Anatoly, and Sebastian, Nicy. "Fractional Integration of the Product of Bessel Functions of the First Kind." Fractional Calculus and Applied Analysis 13.2 (2010): 159-176. <http://eudml.org/doc/219642>.

@article{Kilbas2010,

abstract = {Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50,
33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine and sine functions are given. The results are established in terms of generalized Lau-ricella function due to Srivastava and Daoust. Corresponding assertions for the Riemann-Liouville and Erdélyi-Kober fractional integrals are presented.},

author = {Kilbas, Anatoly, Sebastian, Nicy},

journal = {Fractional Calculus and Applied Analysis},

keywords = {Fractional Integrals; Bessel Function of the First Kind; Generalized Hypergeometric Series; Generalized Lauricella Series in Several Variables; Cosine and Sine Trigonometric Functions; fractional integrals; Bessel function of first kind; generalized hypergeometric series; generalized Lauricella series in several variables; cosine and sine trigonometric functions},

language = {eng},

number = {2},

pages = {159-176},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Fractional Integration of the Product of Bessel Functions of the First Kind},

url = {http://eudml.org/doc/219642},

volume = {13},

year = {2010},

}

TY - JOUR

AU - Kilbas, Anatoly

AU - Sebastian, Nicy

TI - Fractional Integration of the Product of Bessel Functions of the First Kind

JO - Fractional Calculus and Applied Analysis

PY - 2010

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 13

IS - 2

SP - 159

EP - 176

AB - Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50,
33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine and sine functions are given. The results are established in terms of generalized Lau-ricella function due to Srivastava and Daoust. Corresponding assertions for the Riemann-Liouville and Erdélyi-Kober fractional integrals are presented.

LA - eng

KW - Fractional Integrals; Bessel Function of the First Kind; Generalized Hypergeometric Series; Generalized Lauricella Series in Several Variables; Cosine and Sine Trigonometric Functions; fractional integrals; Bessel function of first kind; generalized hypergeometric series; generalized Lauricella series in several variables; cosine and sine trigonometric functions

UR - http://eudml.org/doc/219642

ER -

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