Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform

Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform

In this paper, our leading objective is to relate the fractional integral operator known as Pδ-transform with the ք-extended Mathieu series. We show that the Pδ-transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As coro...

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Main Authors: Hafte Amsalu Kahsay, Adnan Khan, Sajjad Khan, Kahsay Godifey Wubneh
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2021/5523509
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spelling doaj-51b7773d93e5443d882225420c3f65872021-06-21T02:26:00ZengHindawi LimitedAdvances in Mathematical Physics1687-91392021-01-01202110.1155/2021/5523509Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace TransformHafte Amsalu Kahsay0Adnan Khan1Sajjad Khan2Kahsay Godifey Wubneh3Wollo UniversityNational College of Business Administration & EconomicsNational College of Business Administration & EconomicsWollo UniversityIn this paper, our leading objective is to relate the fractional integral operator known as Pδ-transform with the ք-extended Mathieu series. We show that the Pδ-transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the Pδ-transform into a classical Laplace transform by changing the variable lnδ−1s+1/δ−1⟶s; then, we get the integral involving the Laplace transform.http://dx.doi.org/10.1155/2021/5523509
collection DOAJ
language English
format Article
sources DOAJ
author Hafte Amsalu Kahsay
Adnan Khan
Sajjad Khan
Kahsay Godifey Wubneh
spellingShingle Hafte Amsalu Kahsay
Adnan Khan
Sajjad Khan
Kahsay Godifey Wubneh
Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform
Advances in Mathematical Physics
author_facet Hafte Amsalu Kahsay
Adnan Khan
Sajjad Khan
Kahsay Godifey Wubneh
author_sort Hafte Amsalu Kahsay
title Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform
title_short Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform
title_full Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform
title_fullStr Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform
title_full_unstemmed Fractional Operators Associated with the ք-Extended Mathieu Series by Using Laplace Transform
title_sort fractional operators associated with the ք-extended mathieu series by using laplace transform
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9139
publishDate 2021-01-01
description In this paper, our leading objective is to relate the fractional integral operator known as Pδ-transform with the ք-extended Mathieu series. We show that the Pδ-transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the Pδ-transform into a classical Laplace transform by changing the variable lnδ−1s+1/δ−1⟶s; then, we get the integral involving the Laplace transform.
url http://dx.doi.org/10.1155/2021/5523509
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AT adnankhan fractionaloperatorsassociatedwiththekʻextendedmathieuseriesbyusinglaplacetransform
AT sajjadkhan fractionaloperatorsassociatedwiththekʻextendedmathieuseriesbyusinglaplacetransform
AT kahsaygodifeywubneh fractionaloperatorsassociatedwiththekʻextendedmathieuseriesbyusinglaplacetransform
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