On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere

On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere

Diffusion equation has many applications in sciences, not only in physics but also in biology, astrophysics and etc. Especially interest in diffusion in curved surfaces. The last has an application to biological membranes. One of the problems of biophysics is modeling of the transport of substances...

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Main Authors: Rakhimov, Abdumalik A., Akhmedov, Anvarjon
Format: Article
Language:English
Published: Institute Mathematical Sciences, Universiti Putra Malaysia 2012
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/24882/
http://irep.iium.edu.my/24882/
http://irep.iium.edu.my/24882/1/rakhimov.pdf
id iium-24882
recordtype eprints
spelling iium-248822017-11-17T09:19:31Z http://irep.iium.edu.my/24882/ On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere Rakhimov, Abdumalik A. Akhmedov, Anvarjon QA Mathematics Diffusion equation has many applications in sciences, not only in physics but also in biology, astrophysics and etc. Especially interest in diffusion in curved surfaces. The last has an application to biological membranes. One of the problems of biophysics is modeling of the transport of substances in the cell. This process has diffusion character. Diffusion processes in cell are complex phenomenon for modeling. For instant, model can contain fractional derivation by time. In this it is important to determine a fundamental solution of the problem. In this work as a curved surface, we consider N-dimensional sphere and study a fundamental solution of the Cauchy problem for time fractional diffusion equation. Fundamental solutions obtained as a series of distributions by spherical harmonics. Convergence of distribution expansions by spherical harmonics in weak topology is considered. Institute Mathematical Sciences, Universiti Putra Malaysia 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/24882/1/rakhimov.pdf Rakhimov, Abdumalik A. and Akhmedov, Anvarjon (2012) On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere. Malaysian Journal of Mathematical Sciences, 6 (1). pp. 105-112. ISSN 1823-8343 http://einspem.upm.edu.my/journal/fullpaper/vol6no1/7.%20Abdumalik_Anvarjonedit.pdf
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Rakhimov, Abdumalik A.
Akhmedov, Anvarjon
On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere
description Diffusion equation has many applications in sciences, not only in physics but also in biology, astrophysics and etc. Especially interest in diffusion in curved surfaces. The last has an application to biological membranes. One of the problems of biophysics is modeling of the transport of substances in the cell. This process has diffusion character. Diffusion processes in cell are complex phenomenon for modeling. For instant, model can contain fractional derivation by time. In this it is important to determine a fundamental solution of the problem. In this work as a curved surface, we consider N-dimensional sphere and study a fundamental solution of the Cauchy problem for time fractional diffusion equation. Fundamental solutions obtained as a series of distributions by spherical harmonics. Convergence of distribution expansions by spherical harmonics in weak topology is considered.
format Article
author Rakhimov, Abdumalik A.
Akhmedov, Anvarjon
author_facet Rakhimov, Abdumalik A.
Akhmedov, Anvarjon
author_sort Rakhimov, Abdumalik A.
title On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere
title_short On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere
title_full On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere
title_fullStr On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere
title_full_unstemmed On the fundamental solution of the Cauchy problem for time fractional diffusion equation on the sphere
title_sort on the fundamental solution of the cauchy problem for time fractional diffusion equation on the sphere
publisher Institute Mathematical Sciences, Universiti Putra Malaysia
publishDate 2012
url http://irep.iium.edu.my/24882/
http://irep.iium.edu.my/24882/
http://irep.iium.edu.my/24882/1/rakhimov.pdf
first_indexed 2023-09-18T20:37:13Z
last_indexed 2023-09-18T20:37:13Z
_version_ 1777409125882265600

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