On some applications of the space-time fractional derivative

On some applications of the space-time fractional derivative

In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional d...

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Main Authors: Ahmood, Wasan Ajeel, Kilicman, Adem
Format: Article
Language:English
Published: SpringerOpen 2016
Online Access:http://psasir.upm.edu.my/id/eprint/53429/
http://psasir.upm.edu.my/id/eprint/53429/
http://psasir.upm.edu.my/id/eprint/53429/
http://psasir.upm.edu.my/id/eprint/53429/1/On%20some%20applications%20of%20the%20space-time.pdf
id upm-53429
recordtype eprints
spelling upm-534292017-10-30T08:01:59Z http://psasir.upm.edu.my/id/eprint/53429/ On some applications of the space-time fractional derivative Ahmood, Wasan Ajeel Kilicman, Adem In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional derivative is developed to augment the equations. The results show that this method is effective, convenient, and easily executable. The main advantage of the proposed approach is that it is an accurate analytical method (the Laplace transform method) that can be implemented for both space and time discretizations of the fractional derivatives and allows us to present new solutions to problems by certain applications for solving space-time fractional derivatives. SpringerOpen 2016-12 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/53429/1/On%20some%20applications%20of%20the%20space-time.pdf Ahmood, Wasan Ajeel and Kilicman, Adem (2016) On some applications of the space-time fractional derivative. Advances in Difference Equations, 2016 (1). pp. 1-14. ISSN 1687-1839; ESSN: 1687-1847 https://link.springer.com/article/10.1186/s13662-016-1015-z 10.1186/s13662-016-1015-z
repository_type Digital Repository
institution_category Local University
institution Universiti Putra Malaysia
building UPM Institutional Repository
collection Online Access
language English
description In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional derivative is developed to augment the equations. The results show that this method is effective, convenient, and easily executable. The main advantage of the proposed approach is that it is an accurate analytical method (the Laplace transform method) that can be implemented for both space and time discretizations of the fractional derivatives and allows us to present new solutions to problems by certain applications for solving space-time fractional derivatives.
format Article
author Ahmood, Wasan Ajeel
Kilicman, Adem
spellingShingle Ahmood, Wasan Ajeel
Kilicman, Adem
On some applications of the space-time fractional derivative
author_facet Ahmood, Wasan Ajeel
Kilicman, Adem
author_sort Ahmood, Wasan Ajeel
title On some applications of the space-time fractional derivative
title_short On some applications of the space-time fractional derivative
title_full On some applications of the space-time fractional derivative
title_fullStr On some applications of the space-time fractional derivative
title_full_unstemmed On some applications of the space-time fractional derivative
title_sort on some applications of the space-time fractional derivative
publisher SpringerOpen
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/53429/
http://psasir.upm.edu.my/id/eprint/53429/
http://psasir.upm.edu.my/id/eprint/53429/
http://psasir.upm.edu.my/id/eprint/53429/1/On%20some%20applications%20of%20the%20space-time.pdf
first_indexed 2018-09-07T18:21:57Z
last_indexed 2018-09-07T18:21:57Z
_version_ 1610973989382914048

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