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: A. O. Lopushansky, H. P. Lopushanska, O. V. Pasichnyk
Format: Article
Language:English
Published: Vasyl Stefanyk Precarpathian National University 2013-01-01
Series:Karpatsʹkì Matematičnì Publìkacìï
Online Access:http://journals.pu.if.ua/index.php/cmp/article/view/88
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spelling doaj-9136c0b5d2af49d490714eea938bc7422020-11-24T21:45:59ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102013-01-0141728210.15330/cmp.4.1.72-8292Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to timeA. O. Lopushansky0H. P. Lopushanska1O. V. Pasichnyk2Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineIvan Franko National University, 1 Universytetska str., 79000, Lviv, UkraineIvan Franko National University of LvivDifferent 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
collection DOAJ
language English
format Article
sources DOAJ
author A. O. Lopushansky
H. P. Lopushanska
O. V. Pasichnyk
spellingShingle A. O. Lopushansky
H. P. Lopushanska
O. V. Pasichnyk
Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time
Karpatsʹkì Matematičnì Publìkacìï
author_facet A. O. Lopushansky
H. P. Lopushanska
O. V. Pasichnyk
author_sort A. O. Lopushansky
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
2313-0210
publishDate 2013-01-01
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
work_keys_str_mv AT aolopushansky twodefinitionsofthegeneralizedcauchyproblemforsemilineardiffusionequationwithfractionalderivativewithrespecttotime
AT hplopushanska twodefinitionsofthegeneralizedcauchyproblemforsemilineardiffusionequationwithfractionalderivativewithrespecttotime
AT ovpasichnyk twodefinitionsofthegeneralizedcauchyproblemforsemilineardiffusionequationwithfractionalderivativewithrespecttotime
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