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On fractional heat equations with non-local initial conditions

Part of: Parabolic equations and systems Other special functions

Published online by Cambridge University Press:  08 July 2015

Bruno de Andrade ,
Claudio Cuevas  and
Herme Soto
Bruno de Andrade
Affiliation:
Instituto de Ciências Matemáticas e de Computaҫão, Universidade de São Paulo, Campus de São Carlos, CEP 13560-970, São Carlos, São Paulo, Brazil (bruno00luis@gmail.com)
Claudio Cuevas
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco, CEP 50540-740, Recife, Pernambuco, Brazil (cch@dmat.ufpe.br)
Herme Soto
Affiliation:
Departamento de Matemática e Estadística, Universidad de La Frontera, Cosilla 54D Temuco, Chile (hsoto@ufro.cl)
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Abstract

In this paper we consider the problem of existence of mild solutions to semilinear fractional heat equations with non-local initial conditions. We provide sufficient conditions for existence and regularity of such solutions.

Keywords

fractional heat equationsnon-local initial conditionsMittag-Leffler functions

MSC classification

Secondary: 35K05: Heat equation 35K55: Nonlinear parabolic equations 33E12: Mittag-Leffler functions and generalizations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 65 - 76
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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