Fractional calculus pertaining to multivariable I-function defined by Prathima

Kumar, D.; Ayant, F. Y.

doi:10.2478/jamsi-2019-0009

Abstract

In this paper, we study a pair of unified and extended fractional integral operator involving the multivariable I-functions and general class of multivariable polynomials. Here, we use Mellin transforms to obtain our main results. Certain properties of these operators concerning to their Mellin-transforms have been investigated. On account of the general nature of the functions involved herein, a large number of known (may be new also) fractional integral operators involved simpler functions can be obtained. We will also quote the particular case of the multivariable H-function.

References

F. Y. Ayant, An integral associated with the Aleph-functions of several variables, Int. J. Math. Trends Tech. 31(3) (2016), 142–154.10.14445/22315373/IJMTT-V31P522
Search in Google Scholar Back to article
D. Baleanu, D. Kumar and S. D. Purohit, Generalized fractional integrals of product of two H-functions and a general class of polynomials, Int. J. Comput. Math. 93(8) (2016), 1320–1329.10.1080/00207160.2015.1045886
Search in Google Scholar Back to article
B.L.J. Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes integrals, Compos. Math. 15 (1964), 239–341.
Search in Google Scholar Back to article
V.B.L. Chaurasia and A. Srivastava, A unified approach to fractional calculus pertaining to H-functions, Soochow J. Math. 33(2) (2007), 211–221.
Search in Google Scholar Back to article
J. Choi, J. Daiya, D. Kumar and R. K. Saxena, Fractional differentiation of the product of Appell function F₃ and multivariable H-function, Commun. Korean Math. Soc., 31(1) (2016), 115–129.10.4134/CKMS.2016.31.1.115
Search in Google Scholar Back to article
J. Daiya, J. Ram and D. Kumar, The multivariable H-function and the general class of Srivastava polynomials involving the generalized Mellin-Barnes contour integrals, FILOMAT 30(6) (2016), 1457–1464.10.2298/FIL1606457D
Search in Google Scholar Back to article
A. Erdélyi, On some functional transformations, Univ. Politec. Torino, Rend. Sem. Mat. 10 (1950-51), 217-234.
Search in Google Scholar Back to article
D. Kumar and F.Y. Ayant, Some double integrals involving multivariable I-function, Acta Universitatis Apulensis 58(2) (2019), 35–43.10.17114/j.aua.2019.58.03
Search in Google Scholar Back to article
D. Kumar, F.Y. Ayant and J. Choi, Application of product of the multivariable A-function and the multivariable Srivastava polynomials, East Asian Math. J. 34(3) (2018), 295–303.
Search in Google Scholar Back to article
D. Kumar and J. Daiya, Fractional calculus pertaining to generalized H-functions, Glob. J. Sci. Front. Res. (F) 14(3) (2014), 25–35.
Search in Google Scholar Back to article
D. Kumar, R.K. Gupta, B.S. Shaktawat and J. Choi, Generalized fractional calculus formulas involving the product of Aleph-function and Srivastava polynomials, Proc. Jangjeon Math. Soc. 20(4) (2017), 701–717.
Search in Google Scholar Back to article
D. Kumar, S. D. Purohit and J. Choi, Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials, J. Nonlinear Sci. Appl. 9 (2016), 8–21.10.22436/jnsa.009.01.02
Search in Google Scholar Back to article
E.R. Love, Some integral equations involving hypergeometric functions, Proc. Edinb. Math. Soc. 15 (3) (1967), 169–198.10.1017/S0013091500011706
Search in Google Scholar Back to article
J. Prathima, V. Nambisan and S. K. Kurumujji, A study of I-function of several complex variables, Int. J. Engrg. Math. 2014 (2014), 1–12.10.1155/2014/931395
Search in Google Scholar Back to article
J. Ram and D. Kumar, Generalized fractional integration involving Appell hypergeometric function of the product of two H-functions, Vijanana Parishad Anusandhan Patrika 54(3) (2011), 33–43.
Search in Google Scholar Back to article
A.K. Rathie, A new generalization of generalized hypergeometric function, Le Matematiche 52(2) (1997), 297–310.
Search in Google Scholar Back to article
M. Saigo, R.K. Saxena and J. Ram, On the fractional calculus operator associated with the H-function, Ganita Sandesh 6(1) (1992), 36–47.
Search in Google Scholar Back to article
R.K. Saxena and V.S. Kiryakova, On relation between the two-dimensional H-transforms in terms of Erdélyi-Kober operators, Math. Balkanica 6 (1992), 133–140.
Search in Google Scholar Back to article
R.K. Saxena and D. Kumar, Generalized fractional calculus of the Aleph-function involving a general class of polynomials, Acta Math. Sci. Ser. B Engl. Ed. 35(5) (2015), 1095–1110.10.1016/S0252-9602(15)30042-4
Search in Google Scholar Back to article
R.K. Saxena and R.K. Kumbhat, Fractional integration operators of two variables, Proc. Indian Acad. Sci. Math. Sci. 78 (1973), 177–186.10.1007/BF03049477
Search in Google Scholar Back to article
R.K. Saxena and R.K. Kumbhat, Some properties of generalized Kober operators, Vijnana Parishad Anusandhan Patrika 18 (1975), 139–150.
Search in Google Scholar Back to article
R.K. Saxena, J. Ram and D.L. Suthar, Unified fractional derivative formulas for the multivariable H-function, Vijnana Parishad Anusandhan Patrika 49(2) (2006), 159–175.
Search in Google Scholar Back to article
H.M. Srivastava, A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific J. Math. 177 (1985), 183–191.10.2140/pjm.1985.117.183
Search in Google Scholar Back to article
H.M. Srivastava and R. Panda, Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math. 283/284 (1976), 265–274.10.1515/crll.1976.283-284.265
Search in Google Scholar Back to article

Fractional calculus pertaining to multivariable I-function defined by Prathima

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