Geodesic
Fractional Integration of the Product of Bessel Functions of the First Kind
Fractional calculus and applied analysis, Tome 13 (2010) no. 2, pp. 159-176.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

Two 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.
Keywords: Fractional Integrals, Bessel Function of the First Kind, Generalized Hypergeometric Series, Generalized Lauricella Series in Several Variables, Cosine and Sine Trigonometric Functions 
@article{FCAA_2010_13_2_a2,
     author = {Kilbas, Anatoly and Sebastian, Nicy},
     title = {Fractional {Integration} of the {Product} of {Bessel} {Functions} of the {First} {Kind}},
     journal = {Fractional calculus and applied analysis},
     pages = {159--176},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2010_13_2_a2/}
}
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
SP  - 159
EP  - 176
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FCAA_2010_13_2_a2/
LA  - en
ID  - FCAA_2010_13_2_a2
ER  - 
%0 Journal Article
%A Kilbas, Anatoly
%A Sebastian, Nicy
%T Fractional Integration of the Product of Bessel Functions of the First Kind
%J Fractional calculus and applied analysis
%D 2010
%P 159-176
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FCAA_2010_13_2_a2/
%G en
%F FCAA_2010_13_2_a2
Kilbas, Anatoly; Sebastian, Nicy. Fractional Integration of the Product of Bessel Functions of the First Kind. Fractional calculus and applied analysis, Tome 13 (2010) no. 2, pp. 159-176. http://geodesic.mathdoc.fr/item/FCAA_2010_13_2_a2/