R. Taywade - Academia.edu (original) (raw)
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Volume 3 Issue 2 by R. Taywade
Mathematics plays a vital role in the expanding knowledge of science. Laplace as well as Weierstr... more Mathematics plays a vital role in the expanding knowledge of science. Laplace as well as Weierstrass transforms are intimately related to the several indispensable concepts in diverse areas. The convolution of the transform plays an important role in digital signal processing. Seeing the importance of convolution structure of the transform in the development of science. The material I am presenting in this paper is the convolution structure of two dimensional Laplace-Weierstrass transform. Convolution theorem for Laplace-Weierstrass transform is proved also some properties of convolution for Laplace-Weierstrass transform is given.
Papers by R. Taywade
The fractional Hankel transform which is a generalization of the Hankel transform has many applic... more The fractional Hankel transform which is a generalization of the Hankel transform has many applications. In this paper we have derived inversion theorem for the generalized Fractional Hankel transform so that the transform can be used in solving partial differential equations or boundary value problems.
Fractional Mellin transform is one of the flourishing field of active research due to its wide ra... more Fractional Mellin transform is one of the flourishing field of active research due to its wide range of applications. Purpose of this paper is to prove Some properties of fractional Mellin transform and show that fractional Mellin transform is linear but not scale invariant as that of conventional Mellin transform is defined.Also Unitary fractional operator is defined and some of its properties are given.Lastly a linear fractional scale invariant system in terms of its response to a unit impulse and also to show that fractional type convolution as in [3] can be used in dealing these linear fractional scale invariant systems as in case of conventional Mellin transform.
Namias [4] had defined fractionalization of conventional Hankel transform, using the method of ei... more Namias [4] had defined fractionalization of conventional Hankel transform, using the method of eigen values and studied its properties. This paper studies the fractional generalization of generalized Hankel transform, which is the generalization of generalized Hankel transform given by Zemanian [5]. We simply referred it as fractional Hankel transform. First we introduce fractional Hankel transform in the generalized sense. Some properties of the Kernel are discussed and inversion formula for fractional Hankel transform is proved. Generalized operational relations are derived that can be used to solve certain classes of ordinary and partial differential equations. Lastly the values of fractional Hankel transform are obtained for some special functions.
Namias 4 had defined fractionalization of conventional Hankel transform, using the method of eige... more Namias 4 had defined fractionalization of conventional Hankel transform, using the method of eigen values and studied and open the door for the research in fractional integral transform. This paper studies the fractionalization of generalized Hankel transform, as given by Zemanian 5 . We referred it as fractional Hankel transform. First we introduce fractional Hankel transform in the generalized sense. Generalized operational relations are derived that can be used to solve certain classes of ordinary and partial differential equations. Lastly the values of fractional Hankel transform are obtained for some special functions.
In this paper some properties of kernel of Namias fractional Hankel transform are proved and frac... more In this paper some properties of kernel of Namias fractional Hankel transform are proved and fractional Hankel transform is extended in the distributional generalized sense. Testing function space is defined. Analyticity, inversion theorem and uniqueness theorem for the generalized fractional Hankel transform are proved.
The fractional Hankel transform which is a generalization of the Hankel transform has many applic... more The fractional Hankel transform which is a generalization of the Hankel transform has many applications. In this paper we establish the initial and final value theorem for the generalized fractional Hankel transform.
Mathematics plays a vital role in the expanding knowledge of science. Laplace as well as Weierstr... more Mathematics plays a vital role in the expanding knowledge of science. Laplace as well as Weierstrass transforms are intimately related to the several indispensable concepts in diverse areas. The convolution of the transform plays an important role in digital signal processing. Seeing the importance of convolution structure of the transform in the development of science. The material I am presenting in this paper is the convolution structure of two dimensional Laplace-Weierstrass transform. Convolution theorem for Laplace-Weierstrass transform is proved also some properties of convolution for Laplace-Weierstrass transform is given.
The fractional Hankel transform which is a generalization of the Hankel transform has many applic... more The fractional Hankel transform which is a generalization of the Hankel transform has many applications. In this paper we have derived inversion theorem for the generalized Fractional Hankel transform so that the transform can be used in solving partial differential equations or boundary value problems.
Fractional Mellin transform is one of the flourishing field of active research due to its wide ra... more Fractional Mellin transform is one of the flourishing field of active research due to its wide range of applications. Purpose of this paper is to prove Some properties of fractional Mellin transform and show that fractional Mellin transform is linear but not scale invariant as that of conventional Mellin transform is defined.Also Unitary fractional operator is defined and some of its properties are given.Lastly a linear fractional scale invariant system in terms of its response to a unit impulse and also to show that fractional type convolution as in [3] can be used in dealing these linear fractional scale invariant systems as in case of conventional Mellin transform.
Namias [4] had defined fractionalization of conventional Hankel transform, using the method of ei... more Namias [4] had defined fractionalization of conventional Hankel transform, using the method of eigen values and studied its properties. This paper studies the fractional generalization of generalized Hankel transform, which is the generalization of generalized Hankel transform given by Zemanian [5]. We simply referred it as fractional Hankel transform. First we introduce fractional Hankel transform in the generalized sense. Some properties of the Kernel are discussed and inversion formula for fractional Hankel transform is proved. Generalized operational relations are derived that can be used to solve certain classes of ordinary and partial differential equations. Lastly the values of fractional Hankel transform are obtained for some special functions.
Namias 4 had defined fractionalization of conventional Hankel transform, using the method of eige... more Namias 4 had defined fractionalization of conventional Hankel transform, using the method of eigen values and studied and open the door for the research in fractional integral transform. This paper studies the fractionalization of generalized Hankel transform, as given by Zemanian 5 . We referred it as fractional Hankel transform. First we introduce fractional Hankel transform in the generalized sense. Generalized operational relations are derived that can be used to solve certain classes of ordinary and partial differential equations. Lastly the values of fractional Hankel transform are obtained for some special functions.
In this paper some properties of kernel of Namias fractional Hankel transform are proved and frac... more In this paper some properties of kernel of Namias fractional Hankel transform are proved and fractional Hankel transform is extended in the distributional generalized sense. Testing function space is defined. Analyticity, inversion theorem and uniqueness theorem for the generalized fractional Hankel transform are proved.
The fractional Hankel transform which is a generalization of the Hankel transform has many applic... more The fractional Hankel transform which is a generalization of the Hankel transform has many applications. In this paper we establish the initial and final value theorem for the generalized fractional Hankel transform.