• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.115-120
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• 2002

The rigid body properties of a structure may be estimated easily if the mass-line of the structure could be taken exactly. However, the exact mass-line may be hard to be obtained exactly in experiments. The mass line value can be read from the mass line in frequency response function. However, the mass lines in the frequency response function sometimes show the fluctuation with frequency, and it cannot be read correctly. In this paper, the wavelet transform is applied to obtain the good mass line value. The mass line calculated by using wavelet transform has unique value and showed in the range of fluctuated values of frequency response function. The rigid body properties obtained by wavelet transform also showed better results than those by fourier transform.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.9
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• pp.725-730
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• 2002

The rigid body properties of a structure may be estimated easily if the mass-line of the structure could be taken exactly. However, the exact mass-line nay be hard to be obtained exactly in experiments. The mass line value can be read from the mass line in frequency response function. However, the mass lines in the frequency response function sometimes show the fluctuation with frequency, and it cannot be read correctly. In this paper, the wavelet transform is applied to obtain the good mass line value. The mass line calculated by using wavelet transform has unique value and showed in the range of fluctuated values of frequency response function. The rigid body properties obtained by wavelet transform also showed better results than those by fourier transform.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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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.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.187-206
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• 2011

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.423-436
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• 2018

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.545-563
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• 2000

An integral transform with the Bessel function Jv(z) in the kernel is considered. The transform is relatd to a singular Sturm-Liouville problem on a half line. This relation yields a Plancherel's theorem for the transform. A Paley-Wiener-type theorem for the transform is also derived.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.521-535
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• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.