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Tytuł artykułu

Integral transforms involving a generalized k-Bessel function

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Języki publikacji
EN
Abstrakty
EN
The main goal of this study was to look into some new integral transformations that are associated with a generalized k-Bessel function. Integral formulas for the generalized k-Bessel function have been established using the Laplace transform, Euler transform, Whittaker transform, and k-transforms. The results presented here have the potential to be helpful, and some special cases of corollaries are explicitly demonstrated.
Wydawca
Rocznik
Strony
art. no. 20220246
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
  • Department of Mathematics, Al-Aqsa University-Gaza, Gaza Strip, Palestine
  • Department of Mathematics, Al-Azhar University-Gaza, Gaza Strip, Palestine
autor
  • Institut Supérieurd’Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
  • China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
  • Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
  • Department of Mathematics, Al-Azhar University-Gaza, Gaza Strip, Palestine
  • Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
Bibliografia
  • [1] R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulg. Math. 15 (2007), no. 2, 179–192.
  • [2] R. Diaz, C. Ortiz, and E. Pariguan, On the k-gamma, q-distribution, Central Eur. J. Math. 8 (2010), no. 3, 448–458, DOI: https://doi.org/10.2478/s11533-010-0029-0.
  • [3] R. Diaz and C. Teruel, q,k-Generalized gamma and beta functions, J. Nonlinear Math. Phys. 12 (2005), no. 1, 118–134, DOI: https://doi.org/10.2991/jnmp.2005.12.1.10.
  • [4] C. G. Kokologiannaki, Properties and inequalities of generalized k-gamma, beta and zeta functions, Int. J. Contemp. Math. Sci. 5 (2010), no. 14, 653–660.
  • [5] V. Krasniqi, A limit for the k-gamma and k-beta function, Int. Math. Forum 5 (2010), no. 33, 1613–1617.
  • [6] M.G. Bin-Saad, M. J. S. Shahwan, J. A. Younis, H. Aydi, and M. A. Abd El Salam, On Gaussian hypergeometric functions of three variables: somenew integral representations, J. Math. 2022 (2022), 16, DOI: https://doi.org/10.1155/2022/1914498.
  • [7] A. Verma, J.A. Younis, H. Aydi, and M.A. Abd El Salam, Certain recursion formulas for new hypergeometric functions of four variables, Palestine J. Math. 11 (2022), no. 2, 81–97.
  • [8] J. Younis, A. Verma, H. Aydi, K. S. Nisar, and H. Alsamir, Recursion formulas for certain quadruple hypergeometric functions, Adv. Differential Equations 407 (2021), 14 pages, DOI: https://doi.org/10.1186/s13662-021-03561-z.
  • [9] S. Mubeen, Solution of some integral equations involving confluen k-hypergeometric functions, Appl. Math. 4 (2013), no. 7A, 9–11, DOI: https://doi.org/10.4236/am.2013.47A003.
  • [10] S. Mubeen and G. M. Habibullah, An integral representation of some k-hypergeometric functions, Int. Math. Forum. 7 (2012), no. 4, 203–207.
  • [11] R. S. Ali, S. Mubeen, K. S. Nisar, S. Araci, and G. Rahman, Some properties of generalized (s, k)-Bessel function in two variables, J. Math. Computer Sci. 24 (2022), 10–21, DOI: https://doi.org/10.22436/jmcs.024.01.02.
  • [12] M. Mansour, Determining the k-generalized gamma function ( )Γ xk by functional equations, Int. J. Contemp. Math. Sci. 4 (2009), no. 21, 1037–1042.
  • [13] F. Merovci, Power product inequalities for the Γk function, Int. J. Math. Anal. 4 (2010), no. 21, 1007–1012.
  • [14] D. L. Suthar, A. M. Khan, A. Alaria, S. D. Purohit, and J. Singh, Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus, AIMS Math. 5 (2020), no. 2, 1400–1410, DOI: https://doi.org/10.3934/math.2020096.
  • [15] K. S. Nisar, W. A. Khan, and A. H. Abusufian, Certain Integral transforms of k -Bessel function, Palestine J. Math. 7 (2018), no. 1, 161–166.
  • [16] L. G. Romero, G. A. Dorrego, and R. A. Cerutti, The k -Bessel function of first kind, Int. Math. Forum. 38 (2012), no. 7, 1859–1864.
  • [17] S. Mubeen, M. Naz, and G. Rahman, A note on k-hypergeometric differential equations, J. Ineq. Spec. Funct. 4 (2013), no. 3, 38–43. http://www.ilirias.com.
  • [18] K. Nantomah and E. Prempeh, Some inequalities for the k-digamma function, Math. Aterna. 4 (2014), no. 5, 521–525.
  • [19] K.S. Gehlot, Differential equation of k-Besselas function and its properties, Nonlinear Anal. Differential Equations 2 (2014), no. 2, 61–67. DOI: http://dx.doi.org/10.12988/nade.2014.3821.
  • [20] K. S. Gehlot and J. C. Prajapati, Fractional calculus of generalized k-Wright function, J. Fract. Calc. Appl. 4 (2013), 283–289.
  • [21] K. S. Gehlot and S. D. Purohit, Fractional calculus of k-Besselas function, Acta Universitatis Apulensis (2014), no. 38, 273–278.
  • [22] M. Ali, W. M. Khan, and I. A. Khan, On certain integral transform involving generalized Bessel-Maitland function with applications, J. Fract. Calc. Appl. 11 (2020), no. 1, 82–90. http://fcag-egypt.com/Journals/JFCA/.
  • [23] M. Ghayasuddin and W. A. Khan, A new extension of Bessel Maitland function and its properties, Matematicki Vesnik 70 (2018), no. 4, 292–302.
  • [24] W. A. Khan and K. S. Nisar, Unified integral operator involving generalized Bessel-Maitland function, Proc. Jangjeon Mathe. Soc. 21 (2018), no. 3, 339–346, DOI: http://dx.doi.org/10.17777/pjms2018.21.3.339.
  • [25] W. A. Khan and K. S. Nisar, Beta type integral formula associated with Wright generalized Bessel function, Acta Math. Univ. Comenianae 87 (2018), no. 1, 117–125.
  • [26] W. A. Khan, K. S. Nisar, and J. Choi, An integral formula of the Mellin transform type involving the extended Wright Bessel function, Far East J. Math. 102 (2017), no. 11, 2903–2912, DOI: https://doi.org/10.17654/MS102112903.
  • [27] S. R. Mondal and K. S. Nisar, Certain unified integral formulas involving the generalized modified k-Bessel function of first kind, Commun. Korean Math. Soc. 32 (2017), no. 1, 47–53, DOI: https://doi.org/10.4134/CKMS.c160017.
  • [28] K. S. Nisar, W. A. Khan, and M. Ghayasuddin, Certain integral transforms of generalized k -Bessel function, Anal. Theory Appl. 34 (2018), no. 2, 165–174, DOI: https://doi.org/10.4208/ata.
  • [29] I. N. Sneddon, The Use of Integral Transforms, Tata McGraw Hill, New Delhi, 1979.
  • [30] E. T. Whittakar and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, United Kingdom, 1962.
  • [31] A. Erdelyi, W. Magnus, F. Oberhettinger, and F. C. Tricomi, Tables of Integral Transforms, McGraw-Hill, New York, Toronto, London, vol. 2, 1954.
  • [32] A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-function, Theory and Applications, Springer, New York, 2010.
  • [33] E. D. Rainville, Special Functions, Macmillan, New York, 1960.
  • [34] C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. 27 (1928), no. 4, 389–400, DOI: https://doi.org/10.1112/plms/s2-46.1.389.
  • [35] E. M. Wright, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Royal Soc. London Ser. A 238 (1940), no. 795, 423–451, DOI: https://doi.org/10.1098/rsta.1940.0002.
  • [36] H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Disc. Math. 1 (2007), 56–71.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c69cee8d-fb9d-4aa4-bb45-7803825e10a3
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