Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
type: Item
instance of: scholarly article
title: Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
zbMATH Open document ID: 1201.34008
author: Jiqin Deng
author: Lifeng Ma
published in: Applied Mathematics Letters
publication date: 2010-05-21T00:00:00Z
review text: Considered are existence and uniqueness of solutions of the following initial value problems \[ D^\alpha x(t)=f(t,D^\beta x(t)),\, 0<t\leq 1;\quad x^{(k)}=n_k,\,k=0,1,\dots,m-1, \] where \(m-1<\alpha<m,\) \(n-1<\beta<n\) \((m,n\in \mathbb{N},\,m-1>n)\), \(D^\alpha\) stands for the Caputo derivative of order \(\alpha\) and \(f\) is a continuous function defined on \([0,1]\times \mathbb{R}\). The proofs are achieved by means of the contraction mapping principle.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 5710911
zbMATH Keywords: Caputo derivative
zbMATH Keywords: fractional integral
zbMATH Keywords: Banach's contraction principle
reviewed by: Gisèle M. Mophou
MaRDI profile type: Publication
full work available at URL: j.aml.2010.02.007
OpenAlex ID: W1981313876
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DOI: 10.1016/J.AML.2010.02.007
description: scientific article; zbMATH DE number 5710911