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AIMS Mathematics

2020, Volume 5, Issue 6: 7531-7547. doi: 10.3934/math.2020482
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Research article

Integral transforms of an extended generalized multi-index Bessel function

  • 1.
    Department of Mathematics, University of Sargodha, Sargodha, Pakistan
  • 2.
    Department of Mathematics, University of Lahore, Sargodha, Pakistan
  • 3.
    Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Upper Dir, 18000, Pakistan
  • 4.
    Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, KSA
  • 5.
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan
  • 6.
    Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
  • Received: 21 July 2020 Accepted: 20 September 2020 Published: 24 September 2020

  • MSC : 33C10, 33B20, 33C65, 11S80

  • In this paper, we discuss the extended generalized multi-index Bessel function by using the extended beta type function. Then we investigate its several properties including integral representation, derivatives, beta transform, Laplace transform, Mellin transforms, and some relations of extension of extended generalized multi-index Bessel function (E1GMBF) with the Laguerre polynomial and Whittaker functions. Further, we also discuss the composition of the generalized fractional integral operator having Appell function as a kernel with the extension of extended generalized multi-index Bessel function and establish these results in terms of Wright functions.

    Citation: Shahid Mubeen, Rana Safdar Ali, Iqra Nayab, Gauhar Rahman, Thabet Abdeljawad, Kottakkaran Sooppy Nisar. Integral transforms of an extended generalized multi-index Bessel function[J]. AIMS Mathematics, 2020, 5(6): 7531-7547. doi: 10.3934/math.2020482

    Related Papers:

  • In this paper, we discuss the extended generalized multi-index Bessel function by using the extended beta type function. Then we investigate its several properties including integral representation, derivatives, beta transform, Laplace transform, Mellin transforms, and some relations of extension of extended generalized multi-index Bessel function (E1GMBF) with the Laguerre polynomial and Whittaker functions. Further, we also discuss the composition of the generalized fractional integral operator having Appell function as a kernel with the extension of extended generalized multi-index Bessel function and establish these results in terms of Wright functions.


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