Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 2: 1462-1475. doi: 10.3934/math.2020100
Previous Article Next Article
Research article

Fractional calculus of a product of multivariable Srivastava polynomial and multi-index Bessel function in the kernel F3

  • 1.
    Department of Applied Mathematics, Aligarh Muslim University, Aligarh-202002, India
  • 2.
    Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
  • 3.
    Department of Mathematics, Ankara 06790, Cankaya University, Turkey
  • 4.
    Institute of Space Sciences, Magurele-Bucharest, Romania
  • Received: 25 September 2019 Accepted: 08 January 2020 Published: 21 January 2020

  • MSC : 33C20, 33B15

  • In this article our main object to compute image formulas of generalized fractional hypergeometric operators, involving the product of multivariable Srivastava polynomial and multiindex Bessel function. The results obtained provide unification and an extension of known results given earlier by Agarwal and Nieto [1], Agarwal et al. [2] Mishra et al. [18], Saxena and Saigo [26], Suthar et al. [32]. We also consider certain special cases of derived results by specializing suitable value of the parameters.

    Citation: Owais Khan, Nabiullah Khan, Kottakkaran Sooppy Nisar, Mohd. Saif, Dumitru Baleanu. Fractional calculus of a product of multivariable Srivastava polynomial and multi-index Bessel function in the kernel F3[J]. AIMS Mathematics, 2020, 5(2): 1462-1475. doi: 10.3934/math.2020100

    Related Papers:

  • In this article our main object to compute image formulas of generalized fractional hypergeometric operators, involving the product of multivariable Srivastava polynomial and multiindex Bessel function. The results obtained provide unification and an extension of known results given earlier by Agarwal and Nieto [1], Agarwal et al. [2] Mishra et al. [18], Saxena and Saigo [26], Suthar et al. [32]. We also consider certain special cases of derived results by specializing suitable value of the parameters.


    加载中


    [1] P. Agarwal, J. Nieto, Some fractional integral formulas for the Mittag-Leffler type function with four parameters, Open Math., 13 (2015), 537-546.
    [2] P. Agarwal, S. V. Rogosin, J. J. Trujillo, Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions, Proceedings-Mathematical Sciences, 125 (2015), 291-306. doi: 10.1007/s12044-015-0243-6
    [3] S. Ahmed, On the generalized fractional integrals of the generalized Mittag-Leffler function, Springer Plus, 3 (2014), 198.
    [4] D. Baleanu, P. Agarwal, S. D. Purohit, Certain fractional integral formulas inmvolving the product of generalized Bessel functions, The Scientific World Journal, 2013 (2013), 1-9.
    [5] A. Erdélyi, W. Magnus, F. Oberhettinger, et al. Higher Transcendental Functions, New York, 1953.
    [6] C. Fox, The G and H functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc., 98 (1961), 395-429.
    [7] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
    [8] M. Kamarujjama, O. Khan, Computation of new class of integrals involving generalized Galue type Struve function, J. Comput. Appl. Math., 351 (2019), 228-236. doi: 10.1016/j.cam.2018.11.014
    [9] M. Kamarujjama, N. U. Khan, O. Khan, The generalized p-k-Mittag-Leffler function and solution of fractional kinetic equations, J. Anal., 27 (2019), 1029-1046. doi: 10.1007/s41478-018-0160-z
    [10] M. Kamarujjama, N. U. Khan, O. Khan, et al. Extended type k-Mittag-Leffler function and its applications, Int. J. Appl. Comput. Math., 5 (2019), 72.
    [11] M. Kamarujjama, N. U. Khan, O. Khan, Fractional calculus of generalized p-k-Mittag-Leffler function using Marichev-Saigo-Maeda operators, Arab J. Math. Sci., 25 (2019), 156-168.
    [12] O. Khan, N. U. Khan, D. Baleanu, et al. Computable solution of fractional kinetic equations using Mathieu-type series, Adv. Differ. Equ-NY, 2019 (2019), 234.
    [13] A. A. Kilbas, M. Saigo, Fractional calculus of the H-function, Fukuoka Univ. Sci. Rep., 28 (1998), 41-51.
    [14] A. A. Kilbas, N. Sebastian, Generalized fractional integration of Bessel function of the first kind, Integr. Transf. Spec. F., 19 (2008), 869-883. doi: 10.1080/10652460802295978
    [15] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier Amsterdam, 2006.
    [16] V. Kiryakova, The special functions of fractional calculus as generalized fractional calculus operators of some basic functions, Comput. Math. Appl., 59 (2010), 128-141.
    [17] O. L. Marichev, Volterra equation of Mellin convolution type with a horn function in the kernel, Izvestiya Akademii Nauk BSSR Seriya Fiziko-Matematicheskikh Nauk, 1 (1974), 128-129.
    [18] V. N. Mishra, D. L. Suthar, S. D. Purohit, Marichev-Saigo-Maeda fractional calculus operators, Srivastava polynomials and generalized Mittag-Leffler function, Cogent Mathematics & Statistics, 4 (2107), 1320830.
    [19] K. S. Nisar, S. D Purohit, R. K. Parmar, Fractional calculus and certain integrals of generalized multi-index Bessel function, arXiv:1706.08039, 2017.
    [20] S. D. Purohit, D. L. Suthar, S. L. Kalla, Marichev Saigo Maeda fractional integration operators of Bessel, Matematiche (Catania), 61 (2012), 21-32.
    [21] M. Saigo, A remark on integral operators involving the gauss hypergeometric functions, Math. Rep. Coll. Gen. Educ. Kyushu Univ., 11 (1978), 135-143.
    [22] M. Saigo, N. Maeda, More generalization of fractional calculus. In: P. Rusev, I. Dimovski and V. Kiryakova (Eds.) Proceedings of the 2nd International Workshop on Transform Methods and Special Functions, Varna 1996, Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, Sofia, 1998.
    [23] R. K. Saxena, K. Nishimoto, N-fractional calculus of generalized Mittag-Leffler functions, J. Fract. Calc., 37 (2010), 43-52.
    [24] R. K. Saxena, T. K. Pogány, On fractional integration formulae for Aleph function, Appl. Math. Comput., 218 (2011), 985-990.
    [25] R. K. Saxena, J. Ram, D. Kumar, Generalized fractional integration of the product of Bessel functions of first kind, Proceeding of the 9th Annual Conference SSFA, 9 (2010), 15-27.
    [26] R. K. Saxena, M. Saigo, Certain properties of the fractional calculus associated with generalized Mittag-Leffler function, Fract. Calc. Appl. Anal., 8 (2005), 141-154.
    [27] H. M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math., 14 (1972), 1-6.
    [28] H. M. Srivastava, M. Garg, Some integrals involving a general class of polynomials and the multivariable H-function, Rev. Roum. Phys., 32 (1987), 685-692.
    [29] H. M. Srivastava, P. W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Chichester, 1985.
    [30] H. M. Srivastava, R. K. Saxena, Operators of fractional integration and their applications, Appl. Math. Comput., 118 (2001), 1-52.
    [31] D. L. Suthar, H. Hababenon, H. Tadesse, Generalized fractional calculus formulas for a product of Mittag-Leffler function and multivariable polynomials, Int. J. Appl. Comput. Math., 4 (2018), 1-12.
    [32] 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.
    [33] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. Lond. Math. Soc., 10 (1935), 257-270.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(3693) PDF downloads(568) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog