A Filippov's theorem, some existence results and the compactness of solution sets of impulsive fractional order differential inclusions
type: Item
instance of: scholarly article
title: A Filippov's theorem, some existence results and the compactness of solution sets of impulsive fractional order differential inclusions
zbMATH Open document ID: 1263.34010
author: Johnny Henderson
author: Abdelghani Ouahab
published in: Mediterranean Journal of Mathematics
publication date: 2012-11-15T00:00:00Z
review text: The authors show an impulsive version of Filippov's theorem and also establish existence results for a fractional differential inclusion of the form \[ D_\ast^\alpha y(t)\in F(t,y(t))\text{ a.e. } t\in [0,b]\backslash\{t_1,\dotsc, t_m\},\;\alpha\in(0,1], \] \[ y(t_k^+)-y(t_k^-)= I_k(y(t_k^-)), \;k=1,\dotsc, m, \] \[ y(0)=a, \] where \(D_\ast^\alpha\) denotes the Caputo fractional derivative, \(F\) is a set-valued map and \(I_k\) are continuous functions.
reviewed by: Claudio Cuevas
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34A37
zbMATH DE Number: 6107822
zbMATH Keywords: fractional differential inclusions
zbMATH Keywords: fractional derivative
zbMATH Keywords: fractional integral
zbMATH Keywords: Caputo fractional derivatives
zbMATH Keywords: impulsive differential inclusions
MaRDI profile type: Publication
full work available at URL: s00009-011-0141-9
OpenAlex ID: W2032623545
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DOI: 10.1007/S00009-011-0141-9
description: scientific article; zbMATH DE number 6107822