Certain integral Transforms of the generalized Lommel-Wright function
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S. Haq
sirajulhaq007@gmail.com
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K.S. Nisar
ksnisar1@gmail.com
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A.H. Khan
ahkhan.amu@gmail.com
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D.L. Suthar
dlsuthar@gmail.com
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DOI:
https://doi.org/10.4067/S0719-06462019000100049Abstract
The aim of this article is to establish some integral transforms of the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function. Some integrals involving trigonometric, generalized Bessel and Struve functions are also indicated as special cases of our main results.
Keywords
[1] J. Choi and P. Agarwal, Certain unified integrals associated with Bessel functions, Bound. Value Probl., 95, (2013), pages 9.
[2] J. Choi, P. Agarwal, S. Mathur and S.D. Purohit, Certain new integral formulas involving the generalized Bessel function, Bull. Korean Math. Soc., 4, (2014), 995-1003.
[3] J. Choi, K.S. Nisar, Certain families of integral formulas involving Struve function, Bol. Soc. Parana. Mat., 37(3), (2019), 27-35.
[4] R. D Ìiaz and E. Pariguan, On hypergeometric functions and k-Pochhammer symbol, Divulg. Mat., 15, (2007), 179-192.
[5] A. Erde Ìlyi,W. Magnus,F. Oberhettinger and F.G. Tricomi, Tables of Integral Transforms, Vol.2, McGraw-Hill, New York-Toronto-London (1954).
[6] K.S. Gehlot, and J.C. Prajapati, Fractional Calculus of generalized k-wright function, Journal of Fractional Calculus and Applications, 4, (2013), 283-289.
[7] K.S. Gehlot and S.D. Purohit, Fractional Calculus of K-Bessels function , Acta Universitatis Apulensis., 38, (2014), 273-278.
[8] K.B. Kachhia and J.C. Prajapati, On generalized fractional kinetic equations involving general- ized Lommel-Wright functions, Alexandria Engineering Journal (elsevier) 55, (2016), 2953-2957.
[9] J.P. Konovska, Theorems on the convergence of series in generalized Lommel-Wright functions. Fract. Calc. Appl. Anal., 10(1),(2007), 59-74.
[10] Y. Luchko, H. Martinez and J. Trujillo, Fractional Fourier transform and some of its applica- tions, Fract. Calc. Appl. Anal., 11, (2008), ,457-470.
[11] A.M. Mathai, R.K. Saxena and H.J. Haubold, The H-function, Theory and Applications, Springer, New York (2010).
[12] K.S. Nisar, D. Baleanu and M.M. Al Qurashi, Fractional calculus and application of general- ized Struve function, Springer Plus (2016)5:910,DOI 10.1186/s40064-016-2560-3.
[13] K.S. Nisar, G. Rahman, A. Ghaffar, S.A. Mubeen, new class of integrals involving extended Mittag-Leffler function, J. Fract. Calc. Appl., 9 (1), (2018), 222-231.
[14] S.R. Mondal, K.S. Nisar, Certain unified integral formulas involving the generalized modified k-Bessel function of first kind, Commun. Korean Math. Soc., 32(1), (2017), 47–53
[15] K.S. Nisar, W.A. Khan, Beta type integral operator associated with Wright generalized Bessel function, Acta Math. Univ. Comenian. (N.S.) 87(1), 117-125(2018).
[16] G. Rahman, A. Ghaffar, K.S. Nisar, S. Mubben, A new class of integrals involving extended Mittag-Leffler function Journal of Fractional Calculus and Applications, 9(1), (2018), 222-231.
[17] K.S. Nisar, W.A. Khan and A.H. Abusufian, Certain Integral transforms of k-Bessel function, Palest. J. Math., 7(1), (2018), 161-166.
[18] K.S. Nisar, D.L. Suthar, S.D. Purohit, M. Aldhaifallah, Some unified integral associated with the generalized Struve function, Proc. Jangjeon Math. Soc.,20(2), (2017), 261-267.
[19] E.D. Rainville, Special Functions, Macmillan, New York, 1960.
[20] A.K. Rathie, A new generalization of generalized hypergeometric function, Matematiche (Catania), 52(2), (1997), 297-310.
[21] H.M. Srivastava, and H.L. Manocha, A treatise on generating functions, John Wily and Sons (Halsted Press, New York,Ellis Horwood, Chichester), 1984.
[2] J. Choi, P. Agarwal, S. Mathur and S.D. Purohit, Certain new integral formulas involving the generalized Bessel function, Bull. Korean Math. Soc., 4, (2014), 995-1003.
[3] J. Choi, K.S. Nisar, Certain families of integral formulas involving Struve function, Bol. Soc. Parana. Mat., 37(3), (2019), 27-35.
[4] R. D Ìiaz and E. Pariguan, On hypergeometric functions and k-Pochhammer symbol, Divulg. Mat., 15, (2007), 179-192.
[5] A. Erde Ìlyi,W. Magnus,F. Oberhettinger and F.G. Tricomi, Tables of Integral Transforms, Vol.2, McGraw-Hill, New York-Toronto-London (1954).
[6] K.S. Gehlot, and J.C. Prajapati, Fractional Calculus of generalized k-wright function, Journal of Fractional Calculus and Applications, 4, (2013), 283-289.
[7] K.S. Gehlot and S.D. Purohit, Fractional Calculus of K-Bessels function , Acta Universitatis Apulensis., 38, (2014), 273-278.
[8] K.B. Kachhia and J.C. Prajapati, On generalized fractional kinetic equations involving general- ized Lommel-Wright functions, Alexandria Engineering Journal (elsevier) 55, (2016), 2953-2957.
[9] J.P. Konovska, Theorems on the convergence of series in generalized Lommel-Wright functions. Fract. Calc. Appl. Anal., 10(1),(2007), 59-74.
[10] Y. Luchko, H. Martinez and J. Trujillo, Fractional Fourier transform and some of its applica- tions, Fract. Calc. Appl. Anal., 11, (2008), ,457-470.
[11] A.M. Mathai, R.K. Saxena and H.J. Haubold, The H-function, Theory and Applications, Springer, New York (2010).
[12] K.S. Nisar, D. Baleanu and M.M. Al Qurashi, Fractional calculus and application of general- ized Struve function, Springer Plus (2016)5:910,DOI 10.1186/s40064-016-2560-3.
[13] K.S. Nisar, G. Rahman, A. Ghaffar, S.A. Mubeen, new class of integrals involving extended Mittag-Leffler function, J. Fract. Calc. Appl., 9 (1), (2018), 222-231.
[14] S.R. Mondal, K.S. Nisar, Certain unified integral formulas involving the generalized modified k-Bessel function of first kind, Commun. Korean Math. Soc., 32(1), (2017), 47–53
[15] K.S. Nisar, W.A. Khan, Beta type integral operator associated with Wright generalized Bessel function, Acta Math. Univ. Comenian. (N.S.) 87(1), 117-125(2018).
[16] G. Rahman, A. Ghaffar, K.S. Nisar, S. Mubben, A new class of integrals involving extended Mittag-Leffler function Journal of Fractional Calculus and Applications, 9(1), (2018), 222-231.
[17] K.S. Nisar, W.A. Khan and A.H. Abusufian, Certain Integral transforms of k-Bessel function, Palest. J. Math., 7(1), (2018), 161-166.
[18] K.S. Nisar, D.L. Suthar, S.D. Purohit, M. Aldhaifallah, Some unified integral associated with the generalized Struve function, Proc. Jangjeon Math. Soc.,20(2), (2017), 261-267.
[19] E.D. Rainville, Special Functions, Macmillan, New York, 1960.
[20] A.K. Rathie, A new generalization of generalized hypergeometric function, Matematiche (Catania), 52(2), (1997), 297-310.
[21] H.M. Srivastava, and H.L. Manocha, A treatise on generating functions, John Wily and Sons (Halsted Press, New York,Ellis Horwood, Chichester), 1984.
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Published
2019-04-01
How to Cite
[1]
S. . Haq, K. . Nisar, A. . Khan, and . D. . Suthar, “Certain integral Transforms of the generalized Lommel-Wright function”, CUBO, vol. 21, no. 1, pp. 49–60, Apr. 2019.
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