Analysis of a system of fractional differential equations
type: Item
instance of: scholarly article
title: Analysis of a system of fractional differential equations
zbMATH Open document ID: 1058.34002
author: Varsha Daftardar-Gejji
author: Azizollah Babakhani
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors investigate the system of fractional differential equations \[ D^\alpha [\overline {x}(t)- \overline {x}(0)]= A\overline {x}(t), \qquad \overline {x}(0)= \overline {x}_0, \quad 0< \alpha< 1, \] where \(D^\alpha\) denotes the Riemannian-Liouville derivative operator and \(A\) is a square matrix having real entries. They discuss the initial value problem for the nonautonomous nonlinear system \[ D^\alpha [\overline {x}(t)- \overline {x}(0)]= f(t,\overline {x}), \quad \overline {x}(0)= \overline {x}_0. \qquad 0< \alpha< 1. \] The dependence of the solutions on the initial conditions is also studied.
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 2082159
zbMATH Keywords: Riemann-Liouville fractional derivative
zbMATH Keywords: Riemann-Liouville fractional integral
zbMATH Keywords: Mittag-Leffler function
zbMATH Keywords: fractional differential equations
zbMATH Keywords: eigenbasis
zbMATH Keywords: real canonical form
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.013
OpenAlex ID: W2008130934
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DOI: 10.1016/J.JMAA.2004.01.013
description: scientific article; zbMATH DE number 2082159