ON THE GENERALIZED KOBER TYPE FRACTIONAL
q-INTEGRAL OPERATOR INVOLVING A BASIC
ANALOGUE OF H-FUNCTION
Jaime Castillo1, Leda Galue2
1Researching Center, University of La Guajira
Faculty of Engineering, Block 6
Riohacha - 440002, COLOMBIA
2CIMA, University of Zulia
Maracaibo - 4001, VENEZUELA

Abstract

In this paper, the generalized fractional q-integral operator of the Kober type is applied to the basic analogue of the H-function. Results involving the basic hypergeometric functions Jν (x; q), Yν (x; q), Kν (x; q), Hν (x; q), r+1 phi r (·), Mac-Robert's E-function and several elementary q-functions, have been deduced as particular cases of the main result.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 2
Year: 2022

DOI: 10.12732/ijam.v35i2.4

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] R. P. Agarwal, A q-analogue of MacRobert’s generalized E-function, Ganita, 11 (1960), 49-63.
  2. [2] J. Castillo, L. Galué, On a fractional q-integral operator involving the basic analogue of Fox-Wright function, International Journal of Applied Mathematics, 33, No 6 (2020), 969-994; doi: 10.12732/ijam.v33i6.2.
  3. [3] M. Delgado, L. Galué, Fractional q-integral operator involving basic hypergeometric function, Algebras Groups Geom., 25 (2008), 53-74. ON THE GENERALIZED KOBER TYPE FRACTIONAL... 261
  4. [4] L. Galué, Generalized Erdélyi-Kober fractional q-integral operator, Kuwait J. Sci. Eng., 36 (2009), 21-34.
  5. [5] L. Galué, Some results on a fractional q-integral operator involving generalized basic hypergeometric function, Rev. Téc. Ing. Univ. Zulia, 35 (2012), 302-310.
  6. [6] M. Garg, L. Chanchlani, Kober fractional q-derivative operators, Le Matematiche, 66 (2011), 13-26.
  7. [7] G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge (2004).
  8. [8] S.L. Kalla, R.K. Yadav and S.D. Purohit, On the Riemann-Liouville fractional q-integral operator involving a basic analogue of Fox H-function, Fract. Calc. Appl. Anal., 8 (2005), 313-322.
  9. [9] R.K. Saxena, G.C. Modi and S.L. Kalla, A basic analogue of Fox’s Hfunction, Rev. Téc. Ing. Univ. Zulia, 6 (1983), 139-143.
  10. [10] R.K. Saxena, R. Kumar, Recurrence relations for the basic analogue of the H-function, J. Nat. Acad. Math., 8 (1990), 48-54.
  11. [11] R.K. Saxena, R.K. Yadav, S.D. Purohit and S.L. Kalla, Kober fractional q-integral operator of the basic analogue of the H-function, Rev. Téc. Ing. Univ. Zulia, 28 (2005), 154-158.
  12. [12] R. K. Yadav, S. D. Purohit, Application of Riemann-Liouville fractional q-integral operator to basic hypergeometric functions, Acta Ciencia Indica, 30 (2004), 593-600.
  13. [13] R. K. Yadav, S. D. Purohit, On applications of Kober fractional q-integral operator to certain basic hypergeometric functions, J. Rajasthan Acad. Phy. Sci., 5 (2006), 437-448.
  14. [14] R.K. Yadav, S.L. Kalla and G. Kaur, On fractional q-integral operator involving the basic multiple hypergeometric functions, Algebras Groups Geom., 27 (2010), 97-116.