DOI QR코드

DOI QR Code

A NEW CLASS OF EULER TYPE INTEGRAL OPERATORS INVOLVING MULTIINDEX MITTAG-LEFFLER FUNCTION

  • Khan, Nabiullah (Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University) ;
  • Ghayasuddin, Mohd. (Department of Mathematics, Faculty of Science, Integral University) ;
  • Shadab, Mohd (Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University))
  • Received : 2018.04.24
  • Accepted : 2018.09.05
  • Published : 2018.12.25

Abstract

The main object of the present research paper is to establish two (potentially) useful Euler type integrals involving multiindex Mittag-Leffler functions, which are expressed in terms of Wright hypergeometric functions. Some deductions of the main results are also indicated.

Keywords

References

  1. P. Agarwal, S. Jain, S. Agarwal and M. Nagpal; On a new class of integrals involving Bessel functions of the first kind, Comm. Num. Ana.,(2014), 1-7.
  2. Y. A. Brychkov; Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas, CRC Press, Taylor and Francis Group,Boca Raton,London and New York, 2008.
  3. J. Choi, P. Agarwal, S. Mathur and S.D. Purohit; Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc., 51(4)(2014), 995-1003. https://doi.org/10.4134/BKMS.2014.51.4.995
  4. J. Choi and P. Agarwal; Certain unified integrals involving a product of Bessel functions of first kind, Hon. Math. J., 35(4)(2013), 667-677. https://doi.org/10.5831/HMJ.2013.35.4.667
  5. J. Choi and P. Agarwal; Certain Unified Integrals Associated with Bessel functions, Boundary Value Problems, 95(2013), 667-677.
  6. J. Choi, A. Hasanove, H. M. Srivastava and M. Turaev; Integral representations for Srivastava's triple hypergeometric functions, Taiwanese J. Math., 15(6)(2011), 2751-2762. https://doi.org/10.11650/twjm/1500406495
  7. C. Fox; The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. (Ser. 2), 27(1928), 389-400.
  8. R.K. Gupta, B.S. Shaktawat and Dinesh Kumar, A study of Saigo-Maeda fractional calculus operators associated with the Multiparameter K-Mittag-Leffler function, Asian Journal of Mathematics and Computer Research, 12(4)(2016), 243-251.
  9. N.U. Khan, M. Ghayasuddin and T. Usman; On certain integral formulas involving the product of Bessel function and Jacobi polynomial, Tamkang J. Math., 47(3)(2016), 339-349. https://doi.org/10.5556/j.tkjm.47.2016.1968
  10. N.U. Khan, S.W. Khan and M. Ghayasuddin; Some new results associated with the Bessel-Struve kernel function, Acta Univ. Apul., 48(2016), 89-101.
  11. V.S. Kiryakova; Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comp. Appl. Math., 118(2000), 241-259. https://doi.org/10.1016/S0377-0427(00)00292-2
  12. Dinesh Kumar, R.K. Gupta, D.S. Rawat, and J. Daiya, Hypergeometric fractional integrals of multiparameter K-Mittag-Leffler function, Nonlinear Science Letters A: Mathematics, Physics and Mechanics, 9(1)(2018), 17-26.
  13. Dinesh Kumar, R.K. Gupta and D.S. Rawat, MarichevaASSaigoaASMaeda Fractional Differential Operator Involving Mittag-Leffler Type Function with Four Parameters, Journal of Chemical, Biological and Physical Sciences (JCBPS), Section C, 7(2)(2017), 201-210.
  14. Dinesh Kumar; On Certain Fractional Calculus Operators Involving Generalized Mittag-Leffler Function, Sahand Communication in Mathematical Analysis, 3(2)(2016), 33-45.
  15. Dinesh Kumar and S.D. Purohit; Fractional differintegral operators of the generalized Mittag-Leffler type function, Malaya J. Mat., 2(4)(2014), 419-425.
  16. R. Mathur; Integral Representation of Exton's Triple Hypergeometric Series, Int. J. Math. Ana., 6(48)(2012), 2357-2360.
  17. E. D. Rainville; Special Functions, The Macmillan Co. Inc., New York (1960). Reprinted by Chelsea Publ. Co. Bronx,NewYork,(1971)
  18. B.S. Shaktawat, R.K. Gupta and Dinesh Kumar, Generalized fractional Kinetic equations and its solutions involving generalized Mittag-Leffler function, J. Raj. Acad. Phy. Sci., 16(1),(2)(2017), 63-74.
  19. H. M. Srivastava and J. Choi; Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publisher ,Amsterdam,London and New York,(2012).
  20. H. M. Srivastava and P. W. Karlsson; Multiple Gaussian hypergeometric Series, Halsted Press(Ellis Horwood Ltd.,Chichester,U.K.)John Wiley and Sons,New York, Chichester, Brisbane and Toronto, 1985.
  21. E. M. Wright; The asymptotic expansion of the generalized hypergeometric function-I, J. London Math. Soc., 10(1935), 286-293.
  22. E. M. Wright; The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London,A 238(1940), 423-451. https://doi.org/10.1098/rsta.1940.0002
  23. E. M. Wright; The asymptotic expansion of the generalized hypergeometric function-II, Proc. London Math. Soc., 46(2)(1940), 389-408.