Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

BMSA > BMSA Volume 11 > On some Multidimensional Fractional Integral...
< Back to Volume

On some Multidimensional Fractional Integral Operators Involving Multivariable I-Function

Full Text PDF


In the present paper, we study certain multidimensional fractional integral operators involving a general I-function in their kernel. We give five basic properties of these operators, and then establish two theorems and two corollaries, which are believed to be new. These basic theorems exhibit structural relationships between the multidimensional integral transforms. The one- and two-dimensional analogues of these results, which are new and of interest in themselves, can easily be deduced. Special cases of these latter theorems will give rise to certain known results obtained from time to time by several earlier authors.


Bulletin of Mathematical Sciences and Applications (Volume 11)
Y. Singh and N. Kulkarni, "On some Multidimensional Fractional Integral Operators Involving Multivariable I-Function", Bulletin of Mathematical Sciences and Applications, Vol. 11, pp. 12-20, 2015
Online since:
February 2015

Erdelyi, A.; On fractional integration and its application to the theory of Hankel transforms, Quart. J. Math. Oxford Ser. (2)2, (1920), 293-303.

Erdelyi, A.; On some fractional transformations, Univ. Politec. Torino. Rend. Sem. Mat. 10, (1950), 217-234.

Erdelyi, A. et. al.; Higher Transcendental Functions, vol. I, McGraw-Hill, New York (1953).

Erdelyi, A. et. al.; Tables of Integral Transforms, vol. II, McGraw-Hill, New York (1954).

Gupta, K.C., Goyal, S.P. and Handa, S.; Fractional integral operators involving two variables, Univ. Nac. Tucuman Rev. Ser. A 26 , (1976), 159-171.

Handa, S.; A study of generalized functions of one and two variables, Indian J. of Math., (1976), 11-16.

Kober, H.; On fractional integrals and derivatives, Quart. J. Math. Oxford Ser. 2(II), (1940), 193-211.

Kalla, S.L.; Some theorems on fractional integration, Proc. Nat. Acad. Sci. India Sect. A 36, (1966), 1007-1012.

Kalla, S.L.; Some theorems on fractional integration II, Proc. Nat. Acad. Sci. India Sect. 39, (1969), 44-56.

Kalla, S.L.; Fractional integration operators involving generalized hypergeometric functions, Univ. Nac. Tucuman. Rev. Ser. A 20, (1970), 93-100.

Mathur, S.L.; Astudy of boundary value problems and special functions, Proc. Acad. Sci India Sect. A 43, (1974), 56-61.

Pasad, Y.N.; On a multivariable I-function, Vijnana Parishad Anuusandhan Patrika, vol. 29(4), (1986), 231-235.

Saxena, R.K.; On fractional integral operators, Math. Zeitscher. 95, (1967), 288-291.

Saxena, R.K. and Modi, G.C.; Multidimensional fractional integration operators associated with hypergeometric kernels, Nat. Acad. Sci. Lett. 13, (1980), 153-158.

Sneddon, I.N.; Mixed Boundary Value Problems in Potential Theory, North-Holland Publishing Co. , Amsterdam (1966).

Srivastava, H.M. and Buschmann R.G.; Composition of fractional integral operators involving Fox's H-function, Acta Mexicana Ci Tecn 7, (1973), 21-28.

Srivastava, H.M. and Panda, R.; Some bilateral generating functions for a class of generalized polynomials, J. Reine Angew Math. 283/284, (1976), 265-274.

Srivastava, H.M. and Panda, R.; Expansion theorems for the H-function of several complex variables, J. Reine Angew Math 288, (1976), 129-145.

Srivastava, H.M. and Panda, R.; Certain multidimensional integral transformations I and II, Nederl. Akad Wetensch Proc. Ser. A 81, (1978), 118-141.

Srivastava, H.M. , Gupta, K.C. and Goyal, S.P.; The H-function of One and Two Variables With Applications, South Asian Publishers Pvt. Ltd., New Delhi and Madras (1982).

Show More Hide
Cited By:
This article has no citations.