DOI QR코드

DOI QR Code

SOME PROPERTIES OF GENERALIZED BESSEL FUNCTION ASSOCIATED WITH GENERALIZED FRACTIONAL CALCULUS OPERATORS

  • Jana, Ranjan Kumar (Department of Applied Mathematics and Humanities Sardar Vallabhbhai National Institute of Technology) ;
  • Pal, Ankit (Department of Applied Mathematics and Humanities Sardar Vallabhbhai National Institute of Technology) ;
  • Shukla, Ajay Kumar (Department of Applied Mathematics and Humanities Sardar Vallabhbhai National Institute of Technology)
  • Received : 2019.12.20
  • Accepted : 2020.08.05
  • Published : 2021.01.31

Abstract

This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

Keywords

References

  1. L. Galue, A generalized Bessel function, Integral Transforms Spec. Funct. 14 (2003), no. 5, 395-401. https://doi.org/10.1080/1065246031000074362
  2. A. A. Kilbas and M. Saigo, H-transforms, Analytical Methods and Special Functions, 9, Chapman & Hall/CRC, Boca Raton, FL, 2004. https://doi.org/10.1201/9780203487372
  3. V. Kiryakova, On two Saigo's fractional integral operators in the class of univalent functions, Fract. Calc. Appl. Anal. 9 (2006), no. 2, 159-176.
  4. E. Kratzel, Integral transformations of Bessel type, Proceeding of International Conference on Generalized Functions and Operational Calculus, Varna (1975), 148-155.
  5. D. Kumar, P-transforms, Integral Transforms Spec. Funct. 22 (2011), no. 8, 603-616. https://doi.org/10.1080/10652469.2010.536410
  6. A. M. Mathai, A handbook of generalized special functions for statistical and physical sciences, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993.
  7. A. M. Mathai, A pathway to matrix-variate gamma and normal densities, Linear Algebra Appl. 396 (2005), 317-328. https://doi.org/10.1016/j.laa.2004.09.022
  8. A. M. Mathai and H. J. Haubold, Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy, Phys. A 375 (2007), no. 1, 110-122. https://doi.org/10.1016/j.physa.2006.09.002
  9. A. M. Mathai and H. J. Haubold, On generalized distributions and path-ways, Phys. Lett. A 372(2008), 2109- 2113. https://doi.org/10.1016/j.physleta.2007.10.084
  10. A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Halsted Press, New York, 1978.
  11. A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function, Springer, New York, 2010. https://doi.org/10.1007/978-1-4419-0916-9
  12. S. S. Nair, Pathway fractional integration operator, Fract. Calc. Appl. Anal. 12 (2009), no. 3, 237-252.
  13. T. Pohlen, The Hadamard product and universal power series, Ph.D. Thesis, Universitat Trier, Trier, Germany, 2009.
  14. E. D. Rainville, Special Functions, The Macmillan Co., New York, 1960.
  15. E. M. Wright, On the Coefficients of Power Series Having Exponential Singularities, J. London Math. Soc. 8 (1933), no. 1, 71-79. https://doi.org/10.1112/jlms/s1-8.1.71
  16. E. M. Wright, The Asymptotic Expansion of the Generalized Bessel Function, Proc. London Math. Soc. (2) 38 (1935), 257-270. https://doi.org/10.1112/plms/s2-38.1.257