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Fractional Integration of Generalized Bessel Function of the First Kind

[+] Author Affiliations
Pradeep Malik, Saiful R. Mondal, A. Swaminathan

Indian Institute of Technology Roorkee, Roorkee, UT, India

Paper No. DETC2011-48950, pp. 409-418; 10 pages
doi:10.1115/DETC2011-48950
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME

abstract

Generalizing the classical Riemann-Liouville and Erdéyi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.

Copyright © 2011 by ASME

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