Research Article
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Year 2021, Issue: 2, 60 - 73, 30.10.2021
https://doi.org/10.47087/mjm.752726

Abstract

References

  • [1] Agarwal, P; Purohit, S. D. (2013) . The unified pathway fractional integral formulae, Fract. Calc. Appl., 4(9), 1-8.
  • [2] Bairwa, R. K; Sharma, S. C. (2015) . Certain properties and integral transforms of the k-Generalized Mittag-leffler type function journal of the international academy of physical sciences, 19(4), 277-294.
  • [3] Chaudhry, M. A; Qadir, A; Rafiq, M; Zubair, S. M. (1997) . Extension of Euler's beta function, J. Comput. Appl. Math., 78(1),19-32.
  • [4] Chand, M., Prajapati, J.C., Bonyah, E. (2017). Fractional integral and solution of fractional kinetic equation involving k-MittagLeffler function. Trans. A. Razmadze Math. Inst. 171, 144166 (2017)
  • [5] Choi, J; Agrawal, P.(2013). Certain unified integrals associated with special functions, Boundary value problems, Vol. 2013(95).
  • [6] Dorrego, G. A; Cerutti, R. A. (2012). The k-Mittag-Leffler function, Int. J. Contemp. Math. Sci., 7 , 705-716.
  • [7] Ghayasuddin, M; Khan, W. A; Araci, S. (2018). A new extension of Bessel Maitland function and its properties, Matematicki, Vesnik, Mathe. bechnk, 70(4), 292-302.
  • [8] Khan, M. A., Ahmed, S. (2013). On some properties of the generalized Mittag-Leffler function, Springer Plus,2:337.
  • [9] Khan, A. W; Khan, A. I; Ahmad, M. (2020). On Certain integral transforms involving generalized Bessel-Baitland function J. Appl. and Pure Math. Vol. 2 (1-2), 63-78.
  • [10] Luke, Y. L. (1969). The Special functions and their approximations,vol.1, New York, Academic Press.
  • [11] MacRobert, T. M. (1961). Beta functions formulae and integral involving E-function Math. Annalen, 142,450-452.
  • [12] Marichev, O. I. (1983). Handbook of integral transform and higher transcendental function. Theory and algorithm tables, Ellis Horwood, Chichester John Wiley and sons, New York.
  • [13] Mathai, A. M. (2005). A pathway to matrix-variate gamma and normal densities, Linear Algebra appl., 396,317-328.
  • [14] Mathai, A. M; Haubold, H. J. (2007) Pathway model super statistics, trellis statistics and generalized measure of entropy, Phys. A. 375, 110-122.
  • [15] Mathai, A. M; Haubold, H. J. (2008). On generalized distributions and pathways phys. LCH. A. 372, 2019-2113.
  • [16] Mittag-Lexer, G. M, and Sur la. (1903). nouvelle function E alpha(x), C. R .Acad. Sci Paris, 137, 554-558.
  • [17] Nair, S. S. (2009). Pathway fractional integral operator, Fract. Calc. Appl, Anal, 12(3), 237-252.
  • [18] Nisar, K. S; Mondal, S. R. (2016). Pathway fractional integral operators involving k-Struve function, arXIV: 1611; 09157[math. C. A].
  • [19] Nisar, K. S; Mondal, S. R; Agraval, P. (2016). Pathway fractional integral operator associated with Struve function of first kind, Advanced studies in contemporary Mathematics 26, 63-70.
  • [20] Nisar, K. S; Eata, A. F; Dhatallah, M; Choi, J. (2016). fractional calculus of generalized k-Mittag-Leffler function and its application, advanceds differences equations, 1, 304.
  • [21] Rainville, E. D. (1960). Special functions,The Macmillan Company, New York.
  • [22] Prabhakar, T. R. (1971). A singular integral equation with a generalized Mittag-Leffler function in the kernal, Yokohama Math. J., 19, 7-15.
  • [23] Salim, T. O; Faraj, W. (2012). A generalization of Mittag-Leffler function and integral operator associated with fractional calculus, Appl. Math. Comput., 3(5),1-13.
  • [24] Salim, T. O. (2009). Some properties relating to the generalized Mittag-Leffler function, Adv. Appl. Math. Anal., 4, 21-80.
  • [25] Singh. M; Khan. M; Khan A. H. (2016). On some properties of a generalization of Bessel Maitland function, international journal of mathematics trends and technology 14(1), 46-54.
  • [26] Shukla, A.K; Prajapati, J. C. (2007). On a generalization of Mittag-Leffler function and its properties, J. Math. Ann. Appl., 336, 797-811.
  • [27] Watson, G. N. (1962). A treatise on the theory of bessel functions, Cambridge University Press.
  • [28] Wiman, A. (1905). Uber den fundamental satz in der theory der funktionen, Acta Math., 29, 191-201.
  • [29] Wright, E. M. (1935). The asymptotic expansion of the generalized hypergeometric function, J. Lond. Math. Soc, 10, 286-293.
  • [30] Wright, E. M. (1940). The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. R. Soc. Lond. A, 238, 435-451.
  • [31] Wright, E. M. (1940). The asymptotic expansion of the generalized hypergeometric function II, Proc. Lond. Math. Soc, 46, 389.

The pathway integral operator involving extension of k-Bessel-Maitland function

Year 2021, Issue: 2, 60 - 73, 30.10.2021
https://doi.org/10.47087/mjm.752726

Abstract

It has a wide application in the problem of physics, chemistry, biology, engineering and applied sciences. The theory of Bessel functions is intimately connected with the theory of certain types of differential equations. A detail account of applications of Bessel functions are given in the book of Watson [26]. In this present paper, we establish generalized extension of k-Bessel-Maitland function involving pathway integral operator. we obtain certain composition formulas with pathway fractional integral operators. Further more, Some interesting special cases involving Bessel
functions, generalized Bessel functions, generalized Mittag-Leffer functions, generalized k-Mittag-Leffer functions are deduced.\\

References

  • [1] Agarwal, P; Purohit, S. D. (2013) . The unified pathway fractional integral formulae, Fract. Calc. Appl., 4(9), 1-8.
  • [2] Bairwa, R. K; Sharma, S. C. (2015) . Certain properties and integral transforms of the k-Generalized Mittag-leffler type function journal of the international academy of physical sciences, 19(4), 277-294.
  • [3] Chaudhry, M. A; Qadir, A; Rafiq, M; Zubair, S. M. (1997) . Extension of Euler's beta function, J. Comput. Appl. Math., 78(1),19-32.
  • [4] Chand, M., Prajapati, J.C., Bonyah, E. (2017). Fractional integral and solution of fractional kinetic equation involving k-MittagLeffler function. Trans. A. Razmadze Math. Inst. 171, 144166 (2017)
  • [5] Choi, J; Agrawal, P.(2013). Certain unified integrals associated with special functions, Boundary value problems, Vol. 2013(95).
  • [6] Dorrego, G. A; Cerutti, R. A. (2012). The k-Mittag-Leffler function, Int. J. Contemp. Math. Sci., 7 , 705-716.
  • [7] Ghayasuddin, M; Khan, W. A; Araci, S. (2018). A new extension of Bessel Maitland function and its properties, Matematicki, Vesnik, Mathe. bechnk, 70(4), 292-302.
  • [8] Khan, M. A., Ahmed, S. (2013). On some properties of the generalized Mittag-Leffler function, Springer Plus,2:337.
  • [9] Khan, A. W; Khan, A. I; Ahmad, M. (2020). On Certain integral transforms involving generalized Bessel-Baitland function J. Appl. and Pure Math. Vol. 2 (1-2), 63-78.
  • [10] Luke, Y. L. (1969). The Special functions and their approximations,vol.1, New York, Academic Press.
  • [11] MacRobert, T. M. (1961). Beta functions formulae and integral involving E-function Math. Annalen, 142,450-452.
  • [12] Marichev, O. I. (1983). Handbook of integral transform and higher transcendental function. Theory and algorithm tables, Ellis Horwood, Chichester John Wiley and sons, New York.
  • [13] Mathai, A. M. (2005). A pathway to matrix-variate gamma and normal densities, Linear Algebra appl., 396,317-328.
  • [14] Mathai, A. M; Haubold, H. J. (2007) Pathway model super statistics, trellis statistics and generalized measure of entropy, Phys. A. 375, 110-122.
  • [15] Mathai, A. M; Haubold, H. J. (2008). On generalized distributions and pathways phys. LCH. A. 372, 2019-2113.
  • [16] Mittag-Lexer, G. M, and Sur la. (1903). nouvelle function E alpha(x), C. R .Acad. Sci Paris, 137, 554-558.
  • [17] Nair, S. S. (2009). Pathway fractional integral operator, Fract. Calc. Appl, Anal, 12(3), 237-252.
  • [18] Nisar, K. S; Mondal, S. R. (2016). Pathway fractional integral operators involving k-Struve function, arXIV: 1611; 09157[math. C. A].
  • [19] Nisar, K. S; Mondal, S. R; Agraval, P. (2016). Pathway fractional integral operator associated with Struve function of first kind, Advanced studies in contemporary Mathematics 26, 63-70.
  • [20] Nisar, K. S; Eata, A. F; Dhatallah, M; Choi, J. (2016). fractional calculus of generalized k-Mittag-Leffler function and its application, advanceds differences equations, 1, 304.
  • [21] Rainville, E. D. (1960). Special functions,The Macmillan Company, New York.
  • [22] Prabhakar, T. R. (1971). A singular integral equation with a generalized Mittag-Leffler function in the kernal, Yokohama Math. J., 19, 7-15.
  • [23] Salim, T. O; Faraj, W. (2012). A generalization of Mittag-Leffler function and integral operator associated with fractional calculus, Appl. Math. Comput., 3(5),1-13.
  • [24] Salim, T. O. (2009). Some properties relating to the generalized Mittag-Leffler function, Adv. Appl. Math. Anal., 4, 21-80.
  • [25] Singh. M; Khan. M; Khan A. H. (2016). On some properties of a generalization of Bessel Maitland function, international journal of mathematics trends and technology 14(1), 46-54.
  • [26] Shukla, A.K; Prajapati, J. C. (2007). On a generalization of Mittag-Leffler function and its properties, J. Math. Ann. Appl., 336, 797-811.
  • [27] Watson, G. N. (1962). A treatise on the theory of bessel functions, Cambridge University Press.
  • [28] Wiman, A. (1905). Uber den fundamental satz in der theory der funktionen, Acta Math., 29, 191-201.
  • [29] Wright, E. M. (1935). The asymptotic expansion of the generalized hypergeometric function, J. Lond. Math. Soc, 10, 286-293.
  • [30] Wright, E. M. (1940). The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. R. Soc. Lond. A, 238, 435-451.
  • [31] Wright, E. M. (1940). The asymptotic expansion of the generalized hypergeometric function II, Proc. Lond. Math. Soc, 46, 389.
There are 31 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Moin Ahmad This is me

Saurabh Porwal

Publication Date October 30, 2021
Acceptance Date August 26, 2021
Published in Issue Year 2021 Issue: 2

Cite

APA Ahmad, M., & Porwal, S. (2021). The pathway integral operator involving extension of k-Bessel-Maitland function. Maltepe Journal of Mathematics, 3(2), 60-73. https://doi.org/10.47087/mjm.752726
AMA Ahmad M, Porwal S. The pathway integral operator involving extension of k-Bessel-Maitland function. Maltepe Journal of Mathematics. October 2021;3(2):60-73. doi:10.47087/mjm.752726
Chicago Ahmad, Moin, and Saurabh Porwal. “The Pathway Integral Operator Involving Extension of K-Bessel-Maitland Function”. Maltepe Journal of Mathematics 3, no. 2 (October 2021): 60-73. https://doi.org/10.47087/mjm.752726.
EndNote Ahmad M, Porwal S (October 1, 2021) The pathway integral operator involving extension of k-Bessel-Maitland function. Maltepe Journal of Mathematics 3 2 60–73.
IEEE M. Ahmad and S. Porwal, “The pathway integral operator involving extension of k-Bessel-Maitland function”, Maltepe Journal of Mathematics, vol. 3, no. 2, pp. 60–73, 2021, doi: 10.47087/mjm.752726.
ISNAD Ahmad, Moin - Porwal, Saurabh. “The Pathway Integral Operator Involving Extension of K-Bessel-Maitland Function”. Maltepe Journal of Mathematics 3/2 (October 2021), 60-73. https://doi.org/10.47087/mjm.752726.
JAMA Ahmad M, Porwal S. The pathway integral operator involving extension of k-Bessel-Maitland function. Maltepe Journal of Mathematics. 2021;3:60–73.
MLA Ahmad, Moin and Saurabh Porwal. “The Pathway Integral Operator Involving Extension of K-Bessel-Maitland Function”. Maltepe Journal of Mathematics, vol. 3, no. 2, 2021, pp. 60-73, doi:10.47087/mjm.752726.
Vancouver Ahmad M, Porwal S. The pathway integral operator involving extension of k-Bessel-Maitland function. Maltepe Journal of Mathematics. 2021;3(2):60-73.

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