Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time

Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time

Different equivalent definitions of the Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time and with the generalized function in the initial condition are offered. The existence and uniqueness theorem and the representation of the solution of such proble...

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Main Authors: Lopushansky A.O., Lopushanska H.P., Pasichnyk O.V.
Format: Article
Language:English
Published: Vasyl Stefanyk Precarpathian National University 2012-06-01
Series:Karpatsʹkì Matematičnì Publìkacìï
Online Access:http://journals.pu.if.ua/index.php/cmp/article/view/88/77
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spelling doaj-4c0cba74c0e6465e862cd6e69dc358612020-11-25T00:13:53ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272012-06-01417282Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to timeLopushansky A.O.Lopushanska H.P.Pasichnyk O.V.Different equivalent definitions of the Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time and with the generalized function in the initial condition are offered. The existence and uniqueness theorem and the representation of the solution of such problem for linear homogeneous diffusion equation with fractional derivative with respect to time are obtained.http://journals.pu.if.ua/index.php/cmp/article/view/88/77
collection DOAJ
language English
format Article
sources DOAJ
author Lopushansky A.O.
Lopushanska H.P.
Pasichnyk O.V.
spellingShingle Lopushansky A.O.
Lopushanska H.P.
Pasichnyk O.V.
Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
Karpatsʹkì Matematičnì Publìkacìï
author_facet Lopushansky A.O.
Lopushanska H.P.
Pasichnyk O.V.
author_sort Lopushansky A.O.
title Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
title_short Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
title_full Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
title_fullStr Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
title_full_unstemmed Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
title_sort two definitions of the generalized cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
publisher Vasyl Stefanyk Precarpathian National University
series Karpatsʹkì Matematičnì Publìkacìï
issn 2075-9827
publishDate 2012-06-01
description Different equivalent definitions of the Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time and with the generalized function in the initial condition are offered. The existence and uniqueness theorem and the representation of the solution of such problem for linear homogeneous diffusion equation with fractional derivative with respect to time are obtained.
url http://journals.pu.if.ua/index.php/cmp/article/view/88/77
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AT lopushanskahp twodefinitionsofthegeneralizedcauchyproblemforsemilineardiffusionequationwithfractionalderivativewithrespecttotime
AT pasichnykov twodefinitionsofthegeneralizedcauchyproblemforsemilineardiffusionequationwithfractionalderivativewithrespecttotime
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