On certain integrals involving (p, k)-Mittag-Leffler function

Résumé

In the present paper we establish certain integral formulae involving a new generalization of
Mittag-Leffler function {}_{p}E^{\gamma,\delta,\eta}_{k,\lambda,\nu,\tau}(z) which are expressed in terms of generalized Wright function and hypergeometric function. Further some interesting special cases of our main findings are also developed.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Biographie de l'auteur

Mehar Chand, Guru Kashi University, Bathinda, Republic of India
He worked as an Associate Professor in Guru Kashi University, Talwandi Sabo-Bathinda. His research interest includes Integral transforms, Special functions, Integral equations, Statistical distributions, Fractional calculus, generalised functions, and Fractional deferential equations and Mathematical Physics, Computational Mathematics, Cryptography, Elliptic curve cryptography, Public Key Cryptography, Cryptography Algorithms.

Références

P. Agarwal, Pathway fractional integral formulas involving Bessel function of the first kind, Advanced Studies in Contemporary Mathematics, 25(1), 221–231,(2015)

P. Agarwal and M. Chand and S. Jain, Certain integrals involving generalized Mittag-Leffler functions, Proc. Natl. Acad. Sci., Sect. A: Physical Sciences, 85(3), 359–371, (2015)

J. Choi and P. Agarwal, Certain unified integrals associated with Bessel functions, Boundary Value Problems, 95(1), (2013)

J. Choi and P. Agarwal, Certain unified integrals involving a product of Bessel functions of the first kind, Honam Mathematical Journal, 35, , 667–677, (2013)

J. Choi and P. Agarwal, A note on fractional integral operator associated with multiindex Mittag-Leffler functions, Filomat, 30(7), 1931–1939, (2016)

J. Choi and P. Agarwal and S. Mathur and S.D. Purohit, Certain new integral formulas involving the generalized Bessel functions, Bull. Korean Math. Soc., 51(4), 995-1003, (2014)

R. Diaz and E. Pariguan, On hypergeometric functions and k-Pochhammer symbo, Divulgaciones Mathematicas, 15(2), 179-192, (2007)

C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London. Math. Soc., 27(2), 389-400, (1928)

K. S. Gehlot, Two parameter gamma function and its properties, ”arXiv:1701.01052v1 [math.CA] 3 Jan 2017”,

A. Gupta and C. L. Parihar, On solutions of generalized kinetic equations of fractional order, Bol. Soc. Paran. Mat., 32(1), 181-189, (2014)

N.U. Khan and T. Kashmin, Some integrals for the generalized Bessel-Maitland function, Electronic Journal of Mathematical Analysis and Applications, 4(2), 139-149, (2016)

W.A. Khan and K. S. Nisar, An integral formula of the Mellin transform type involving the extended Wright-Bessel function, Far East Journal of Mathematical Sciences (FJMS), 102(11), 2903-2912, (2017)

A.A Kilbas and M. Saigo and R.K Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators, Inte. Trans. Spec. funct., 15, 31-49, (2004)

Kilbas, A. A. and Srivastava, H. M. and Trujillo, J. J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York,(2006)

Marichev, O. I., Handbook of Integral Transforms and Higher Transcendental Functions, Ellis, Horwood, Chichester (JohnWiley and Sons); New York, (1983)

Mathai, A.M. and Saxena, R.K. and Haubold, H.J., The H-Functions: Theory and Applications, Springer: New York, NY, USA, (2010)

G. M. Mittag-Leffler, Sur la nouvelle function Eα(x), C.R. Acad. Sci. Paris, 137, 554-558, (1903)

Oberhettinger, F. , Tables of Mellin Transforms, Springer, New York,(1974)

T. R. Prabhakar, A Singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J.,19, 7-15, (1971)

Rainville, E. D., Special Functions, The Macmillan Company, New York, (1960)

T. O. Salim, Some properties relating to generalized Mittag-Leffler function, Adv. Appl. Math. Anal, 4(1), 21-30, (2009)

T. O. Salim and A. W. Faraj, A generalization of Mittag-Leffler function and Integral operator associated with Fractional calculus, Journal of Fractional Calculus and Applications, 3(5), 1-13, (2012)

Samko, S. G. and Kilbas, A. A. and Marichev, O. I., Fractional Integrals and Derivatives: Theory and Applications, (1993)

A. K. Shukla and J. C. Prajapati, On a generalized Mittag-Leffler function and its properties, J. Math. Anal. Appl., 336, 797-811, (2007)

H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York., (2012)

Srivastava, H. M. and Karlsson, P. W. Multiple Gaussian Hypergeometric Series, Halsted Press, (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1985)

H.M. Srivastava and Z. Tomovski, ˇ Fractional calculus with an integral operator containing generalized Mittag-Leffler function in the kernel, Appl. Math. Comput., 211(1), 198-210, (2009)

D. L. Suthar, H. Amsalu and K. Godifey, Certain integral involving multivariate Mittag-Leffler function, Journal of Inequalities and Applications,208, (2019)

A. Wiman, U¨berden Fundamentalsatz in der Theorie der Funcktionen, Eα(x), Acta Math., 29, 191-201, (1905)

E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc., 10, 286-293, (1935)

E. M. Wright, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London A, 238, 423-451, (1940)

E. M. Wright, The asymptotic expansion of the generalized hypergeometric function II, Proc. London Math. Soc., 46(2), 389-408, (1940)

Publiée
2025-02-12
Rubrique
Research Articles