• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1169-1177
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• 2016

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.999-1014
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• 2003

For a fixed function h we deal with a class of convolution transforms $f\;{\rightarrow}\;f\;*\;h$, where $(f\;*\;h)(x)\;=\frac{1}{2x}\;{\int_{{R_{+}}^2}}^{e^1{\frac{1}{2}}(x\frac{u^2+y^2}{uy}+\frac{yu}{x})}\;f(u)h(y)dudy,\;x\;\in\;R_{+}$ as integral operators $L_p(R_{+};xdx)\;\rightarrow\;L_r(R_{+};xdx),\;p,\;r\;{\geq}\;1$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $L_2(R_{+};xdx)$ are obtained.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.7-16
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• 2018

The main objective of this paper is to demonstrate how one can obtain very quickly so far unknown Laplace transforms of rather general cases of the generalized hypergeometric function $_3F_3$ by employing generalizations of classical summation theorems for the series $_3F_2$ available in the literature. Several new as well known results obtained earlier by Kim et al. follow special cases of main findings.

• 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.

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.669-675
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• 2021

A GN model with and without energy dissipations is used to discuss the waves propagation in a two-dimension orthotropic half space by the eigenvalues approach. Using the Laplace-Fourier integral transforms to get the solutions of the problem analytically, the basic formulations of the two-dimension problem are given by matrices-vectors differential forms, which are then solved by the eigenvalues scheme. Numerical techniques are used for the inversion processes of the Laplace-Fourier transform. The results for physical quantities are represented graphically. The numerical outcomes show that the characteristic time of pulse heat flux have great impacts on the studied fields values.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.57-69
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• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.467-475
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• 2013

We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We introduce some set CG of symbols and we prove that Toeplitz operators induced by elements of CG are bounded and characterize when Toeplitz operators are compact and show that each element of CG is related with a Carleson measure.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.305-315
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• 1995

The class $R_{\gamma-1,p}(A,B,\alpha)$ for $-1 \leq B < A \leq 1,\gamma > (B -1)p+(A_B)(p-\alpha)/1-B$ and $0 \leq \alpha < p$ consisting of p-valently analytic functions in the open unit disc is defined with the help of convolution technique. We study containment property, integral transforms and a sufficient condition for an analytic function to be in $R_{\gamma-1,p}(A,B,\alpha)$.