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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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    [1] G. Dattoli, S. Lorenzutta, G. Maino, et al. Generalized Bessel functions and exact solutions of partial differential equations, Rend. Mat., 7 (1992), 12.
    [2] V. S. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comput. Appl. Math., 118 (2000), 241-259.
    [3] M. Kamarujjama, Computation of new class of integrals involving generalized Galue type Struve function, J. Comput. Appl. Math., 351 (2019), 228-236.
    [4] O. Khan, M. Kamarujjama, N. U. Khan, Certain integral transforms involving the product of Galue type struve function and Jacobi polynomial, Palestine J. Math., 8 (2019), 191-199.
    [5] M. Kamarujjama, N. U. Khan, O. Khan, The generalized pk-Mittag-Leffler function and solution of fractional kinetic equations, J. Anal., 27 (2019), 1029-1046.
    [6] N. U. Khan, M. Ghayasuddin, W. A. Khan, et al. Certain unified integral involving Generalized Bessel-Maitland function, South East Asian J. Math. Math. Sci., 11 (2015), 27-36.
    [7] N. U. Khan, M. Ghayasuddin, Study of the unified double integral associated with generalized Bessel-Maitland function, Pure Appl. Math. Lett., 2016 (2016), 15-19.
    [8] S. D. Purohit, P. Agarwal, et al. Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc., 51 (2014), 995-1003.
    [9] G. Dattoli, S. Lorenzutta, G. Maino, et al. Theory of multiindex multivariable Bessel functions and Hermite polynomials, Le Mat., 52 (1997), 179-197.
    [10] J. Choi, P. Agarwal, A note on fractional integral operator associated with multiindex MittagLeffler functions, Filomat, 30 (2016), 1931-1939.
    [11] M. Kamarujjama, N. U. Khan, O. Khan, Estimation of certain integrals with extended multi-index Bessel function, Malaya J. Mat. (MJM), 7 (2019), 206-212.
    [12] D. L. Suthar, S. D. Purohit, R. K. Parmar, Generalized fractional calculus of the multi-index Bessel function, Math. Nat. Sci., 1 (2017), 26-32.
    [13] K. S. Nisar, S. D. Purohit, D. L. Suthar, et al. Fractional calculus and certain integrals of generalized multiindex Bessel function, arXiv preprint arXiv: 1706.08039, 2017.
    [14] D. L. Suthar, T. Tsagye, Riemann-Liouville fractional integrals and differential formula involving Multi-index Bessel-function, Math. Sci. Lett., 6 (2017), 233-237.
    [15] D. L. Suthar, D. Kumar, H. Habenom, Solutions of fractional Kinetic equation associated with the generalized multiindex Bessel function via Laplace transform, Differ. Equ. Dyn. Syst., (2019), 1-14.
    [16] O. I. Marichev, Volterra equation of Mellin convolution type with a Horn function in the kernel, Izv. Akad. Nauk BSSR. Ser. Fiz.-Mat. Nauk, 1 (1974), 128-129.
    [17] F. W. Olver, D. W. Lozier, R. F. Boisvert, et al. NIST handbook of mathematical functions hardback and CD-ROM, Cambridge university press, 2010.
    [18] S. Mubeen, R. S. Ali, Fractional operators with generalized Mittag-Leffler k-function, Adv. Differ. Equ., 2019 (2019), 520.
    [19] A. Petojevic, A note about the Pochhammer symbols, Math. Moravica, 12 (2008), 37-42.
    [20] M. A. Chaudhry, A. Qadir, H. M. Srivastava, et al. Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 159 (2004), 589-602.
    [21] M. A. Chaudhry, S. M. Zubair, et al. On a class of incomplete gamma functions with applications, CRC press, 2001.
    [22] H. M. Srivastava, P. W. Karlsson, Multiple gaussian hypergeometric series, Halsted Press (Ellis Horwood Limited, Chichester), 1985.
    [23] D. V. Widder, Laplace transform (PMS-6), Princeton university press, 2015.
    [24] I. N. Sneddon, The use of integral transform, Tata McGraw Hill, New Delhi, 1979.
    [25] M. A. Özarslan, B. Yilmaz, The extended Mittag-Leffler function and its properties, J. Inequal. Appl., 2014 (2014), 85.
    [26] M. A. Özarslan, Some remarks on extended hypergeometric, extended confluent hypergeometric and extended Appell's functions, J. Comput. Anal. Appl., 14 (2012).
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