• 대한수학회논문집
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• 제35권1호
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.

• 대한수학회보
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• 제52권5호
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• pp.1607-1619
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• 2015

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.307-313
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• 2006

In this paper, we first establish an interesting new finite integral whose integrand involves the product of a general class of polynomials introduced by Srivastava [13] and the generalized H-function ([9], [10]) having general argument. Next, we present five special cases of our main integral which are also quite general in nature and of interest by themselves. The first three integrals involve the product of $\bar{H}$-function with Jacobi polynomial, the product of two Jacobi polynomials and the product of two general binomial factors respectively. The fourth integral involves product of Jacobi polynomial and well known Fox's H-function and the last integral involves product of a Jacobi polynomial and 'g' function connected with a certain class of Feynman integral which may have practical applications.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.235-245
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• 2006

Applications of Weyl fractional $q$-integral operator to various generalized basic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper. Certain interesting special cases have also been deduced.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.519-527
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• 2007

In this paper, we establish a theorem wherein we have obtained the image of modified H-transform under the fractional integral operator involving Foxs H-function. Three corollaries of this theorem have also been derived. Further, we obtain one interesting integral by the application of the third corollary. The importance of above findings lies in the fact that our main theorem involves Fox H-function which is very general in nature. The result obtained earlier by Tariq (1998) is a special case of our main findings.

• 대한수학회지
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• 제13권1호
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• pp.15-18
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• 1976

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.229-235
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• 2010

In the present paper, we obtain a new formula for the generalized Weyl differintegral operator in a compact form avoiding the occurrence of infinite series and thus making it useful in applications. Our findings provide interesting generalizations and unifications of the results given by several authors and lying scattered in the literature.

• 대한수학회논문집
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• 제36권1호
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• pp.41-50
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• 2021

This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.257-262
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• 1978

In this paper, we obtain two new double infinite series for the H-function of two variables, by which we also obtain a single infinite series involving the H-function of two variable3. On account of the most general nature of the H-functin of two variables, a number of related double infinite series for simpler functions follow as special cases of our results. As an illustration, we obtain here from one of our main series, the corresponding series for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function and Fox's H-function. A number of other series involving a very large, spectrum of special functions also follow as special cases of our main series but, we are not recording them here for want of space.