Neşe Dernek - Academia.edu (original) (raw)

Papers by Neşe Dernek

Filomat

In this paper the authors gave an iteration identity for the generalized Laplace transform L2n an... more In this paper the authors gave an iteration identity for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Using this identity a Parseval-Goldstein type theorem for the L2n-transform and the G2n-transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given.

DergiPark (Istanbul University), Feb 29, 2012

Konuralp Journal of Mathematics (KJM), Apr 15, 2019

This paper discusses the generalized Mellin transforms and their properties with examples and app... more This paper discusses the generalized Mellin transforms and their properties with examples and applications to integral and partial differential equations. Several simple lemmas and theorems dealing with general properties of the generalized Mellin transform are proved. The main focus of this paper is to develop the method of the generalized Mellin transform to solve partial differential equations and integral equations in applied mathematics.

Gazi University Journal of Science

In this paper, Parseval-Goldstein type theorems involving the G ̃n-integral transform which is mo... more In this paper, Parseval-Goldstein type theorems involving the G ̃n-integral transform which is modified from G_2n-integral transform [7] and the -integral transform [8] are examined. Then, theorems in this paper are shown to yield a number of new identities involving several well-known integral transforms. Using these theorems and their corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Generalizations of Riemann-Liouville and Weyl fractional integral operators are also defined. Some theorems relating generalized Laplace transform, generalized Widder Potential transform, generalized Hankel transform and generalized Bessel transform are obtained. Some illustrative examples are given as applications of these theorems and their results.

Some properties of the Dawson Integral are presented first in the current work, followed by the i... more Some properties of the Dawson Integral are presented first in the current work, followed by the introduction of the Dawson Integral Transform. Iteration identities and relationships, similar to the Parseval Goldstein type, are established involving various well-known integral transforms, such as the Laplace Transform, the L 2 -Transform, and the Dawson Integral for the new integral transform. Furthermore, improper integrals of well-known functions, including the Dawson Integral, Exponential Integral, and the Macdonald Function, are evaluated using the results obtained.

Istanbul University - DergiPark, 2000

In this paper, a solution is given for the following singular Cauchy prob lem: Au = uu + (at +-)u... more In this paper, a solution is given for the following singular Cauchy prob lem: Au = uu + (at +-)ut u{x,Q) = f(x),ut(x,0) = 0. The solution is an uniformly and absolutely convergent power series. Where a,b € R,f(x) is a continuously differentiable function.

In the present paper the authors introduce the E -transform with kernel the exponential integral ... more In the present paper the authors introduce the E -transform with kernel the exponential integral function. It is shown that the third iterate of the L -transform is the exponential integral transform, and some identities involving the new transform, the L -transform and the Widder potential transform are given. Using the identities, Parseval-Goldstein type results involving these transforms are proved. Some illustrative examples are also given. © 2006 Elsevier Inc. All rights reserved. 2, 1 2

In the present paper the authors show that an iteration of the L 2-transform by itself is a const... more In the present paper the authors show that an iteration of the L 2-transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for L 2-transform and the Glasser transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Journal of Mathematical Analysis and Applications, 2009

Integral Transforms and Special Functions, 2011

In the present paper the authors consider the P ν,2-transform as a generalization of the Widder p... more In the present paper the authors consider the P ν,2-transform as a generalization of the Widder potential transform and the Glasser transform. The P ν,2-transform is obtained as an iteration of the the L 2-transform with itself. Many identities involving these transforms are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Applied Mathematics and Computation, 2007

This article was originally published in a journal published by Elsevier, and the attached copy i... more This article was originally published in a journal published by Elsevier, and the attached copy is provided by Elsevier for the author's benefit and for the benefit of the author's institution, for non-commercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues that you know, and providing a copy to your institution's administrator.

Applied Mathematics and Computation, 2006

In the present paper the authors introduce the exponential integral transform and the complementa... more In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltjes transform are given. Using the identities, Parseval-Goldstein type results involving these transforms are proved. Some illustrative examples are also given.

Applied Mathematics and Computation, 2008

In the present paper, the authors introduce several new integral transforms inclu- ding the Ln-tr... more In the present paper, the authors introduce several new integral transforms inclu- ding the Ln-transform, the L2n-transform and P2n-transform generalizations of the classical Laplace transform and the classical Stieltjes tr ansform as respectively. It is shown that the second iterate of the L2n-transform is essentially the P2n-transform. Using this relationship, a few new Parseval-Goldstein type identities are obtained. The theorem and the lemmas that are proven in this article are new useful relations for evaluating infinite integrals of special functions. Some re lated illustrative examples are also given.

The Journal Of Mathematics, Physics and Astronomy, 2000

This paper discusses the generalized Mellin transforms and their properties with examples and app... more This paper discusses the generalized Mellin transforms and their properties with examples and applications to integral and partial differential equations. Several simple lemmas and theorems dealing with general properties of the generalized Mellin transform are proved. The main focus of this paper is to develop the method of the generalized Mellin transform to solve partial differential equations and integral equations in applied mathematics.

In the present paper the authors show that an iteration of the L 2-transform by itself is a const... more In the present paper the authors show that an iteration of the L 2-transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for L 2-transform and the Glasser transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Hacettepe Journal of Mathematics and Statistics, 2020

In the present article, using the generalized Bessel-Maitland transform, the Laplace transform an... more In the present article, using the generalized Bessel-Maitland transform, the Laplace transform and the other known transforms, authors obtain new Parseval-Goldstein type relations. Using these relations, some generalized integrals involving Fox-Wright functions are evaluated. Illustrative examples are also given.

In this paper, authors introduce the generalized Bessel-Maitland transform whose kernel is the ge... more In this paper, authors introduce the generalized Bessel-Maitland transform whose kernel is the generalized Bessel-Maitland function. New identities are obtained for special cases of the generalized Bessel-Maitland function. Using these relations, several identities are obtained for generalized Bessel-Maitland integral transform. It is shown that some special cases of them are related with the Laplace transform and the Hankel transform. Also, some examples are given as representations of the outcomes presented here.

Filomat

In this paper the authors gave an iteration identity for the generalized Laplace transform L2n an... more In this paper the authors gave an iteration identity for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Using this identity a Parseval-Goldstein type theorem for the L2n-transform and the G2n-transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given.

DergiPark (Istanbul University), Feb 29, 2012

Konuralp Journal of Mathematics (KJM), Apr 15, 2019

This paper discusses the generalized Mellin transforms and their properties with examples and app... more This paper discusses the generalized Mellin transforms and their properties with examples and applications to integral and partial differential equations. Several simple lemmas and theorems dealing with general properties of the generalized Mellin transform are proved. The main focus of this paper is to develop the method of the generalized Mellin transform to solve partial differential equations and integral equations in applied mathematics.

Gazi University Journal of Science

In this paper, Parseval-Goldstein type theorems involving the G ̃n-integral transform which is mo... more In this paper, Parseval-Goldstein type theorems involving the G ̃n-integral transform which is modified from G_2n-integral transform [7] and the -integral transform [8] are examined. Then, theorems in this paper are shown to yield a number of new identities involving several well-known integral transforms. Using these theorems and their corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Generalizations of Riemann-Liouville and Weyl fractional integral operators are also defined. Some theorems relating generalized Laplace transform, generalized Widder Potential transform, generalized Hankel transform and generalized Bessel transform are obtained. Some illustrative examples are given as applications of these theorems and their results.

Some properties of the Dawson Integral are presented first in the current work, followed by the i... more Some properties of the Dawson Integral are presented first in the current work, followed by the introduction of the Dawson Integral Transform. Iteration identities and relationships, similar to the Parseval Goldstein type, are established involving various well-known integral transforms, such as the Laplace Transform, the L 2 -Transform, and the Dawson Integral for the new integral transform. Furthermore, improper integrals of well-known functions, including the Dawson Integral, Exponential Integral, and the Macdonald Function, are evaluated using the results obtained.

Istanbul University - DergiPark, 2000

In this paper, a solution is given for the following singular Cauchy prob lem: Au = uu + (at +-)u... more In this paper, a solution is given for the following singular Cauchy prob lem: Au = uu + (at +-)ut u{x,Q) = f(x),ut(x,0) = 0. The solution is an uniformly and absolutely convergent power series. Where a,b € R,f(x) is a continuously differentiable function.

In the present paper the authors introduce the E -transform with kernel the exponential integral ... more In the present paper the authors introduce the E -transform with kernel the exponential integral function. It is shown that the third iterate of the L -transform is the exponential integral transform, and some identities involving the new transform, the L -transform and the Widder potential transform are given. Using the identities, Parseval-Goldstein type results involving these transforms are proved. Some illustrative examples are also given. © 2006 Elsevier Inc. All rights reserved. 2, 1 2

In the present paper the authors show that an iteration of the L 2-transform by itself is a const... more In the present paper the authors show that an iteration of the L 2-transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for L 2-transform and the Glasser transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Journal of Mathematical Analysis and Applications, 2009

Integral Transforms and Special Functions, 2011

In the present paper the authors consider the P ν,2-transform as a generalization of the Widder p... more In the present paper the authors consider the P ν,2-transform as a generalization of the Widder potential transform and the Glasser transform. The P ν,2-transform is obtained as an iteration of the the L 2-transform with itself. Many identities involving these transforms are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Applied Mathematics and Computation, 2007

This article was originally published in a journal published by Elsevier, and the attached copy i... more This article was originally published in a journal published by Elsevier, and the attached copy is provided by Elsevier for the author's benefit and for the benefit of the author's institution, for non-commercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues that you know, and providing a copy to your institution's administrator.

Applied Mathematics and Computation, 2006

In the present paper the authors introduce the exponential integral transform and the complementa... more In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltjes transform are given. Using the identities, Parseval-Goldstein type results involving these transforms are proved. Some illustrative examples are also given.

Applied Mathematics and Computation, 2008

In the present paper, the authors introduce several new integral transforms inclu- ding the Ln-tr... more In the present paper, the authors introduce several new integral transforms inclu- ding the Ln-transform, the L2n-transform and P2n-transform generalizations of the classical Laplace transform and the classical Stieltjes tr ansform as respectively. It is shown that the second iterate of the L2n-transform is essentially the P2n-transform. Using this relationship, a few new Parseval-Goldstein type identities are obtained. The theorem and the lemmas that are proven in this article are new useful relations for evaluating infinite integrals of special functions. Some re lated illustrative examples are also given.

The Journal Of Mathematics, Physics and Astronomy, 2000

This paper discusses the generalized Mellin transforms and their properties with examples and app... more This paper discusses the generalized Mellin transforms and their properties with examples and applications to integral and partial differential equations. Several simple lemmas and theorems dealing with general properties of the generalized Mellin transform are proved. The main focus of this paper is to develop the method of the generalized Mellin transform to solve partial differential equations and integral equations in applied mathematics.

In the present paper the authors show that an iteration of the L 2-transform by itself is a const... more In the present paper the authors show that an iteration of the L 2-transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for L 2-transform and the Glasser transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Hacettepe Journal of Mathematics and Statistics, 2020

In the present article, using the generalized Bessel-Maitland transform, the Laplace transform an... more In the present article, using the generalized Bessel-Maitland transform, the Laplace transform and the other known transforms, authors obtain new Parseval-Goldstein type relations. Using these relations, some generalized integrals involving Fox-Wright functions are evaluated. Illustrative examples are also given.

In this paper, authors introduce the generalized Bessel-Maitland transform whose kernel is the ge... more In this paper, authors introduce the generalized Bessel-Maitland transform whose kernel is the generalized Bessel-Maitland function. New identities are obtained for special cases of the generalized Bessel-Maitland function. Using these relations, several identities are obtained for generalized Bessel-Maitland integral transform. It is shown that some special cases of them are related with the Laplace transform and the Hankel transform. Also, some examples are given as representations of the outcomes presented here.