The existence and uniqueness of a class of fractional differential equations
type: Item
instance of: scholarly article
title: The existence and uniqueness of a class of fractional differential equations
zbMATH Open document ID: 1470.34010
DOI: 10.1155/2014/486040
author: Zhanbing Bai
author: Sujing Sun
author: Yangquan Chen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, \(D_{0 +}^q x(t) = f(t, x(t), D_{0 +}^{q - 1} x(t)), t \in(0, T), \)\(x(0) = 0, D_{0 +}^{q - 1} x(0) = x_0, \) are discussed, where \(f \in C([0, T] \times \mathbb{R}^2, \mathbb{R}), D_{0 +}^q x(t)\) is the standard Riemann-Liouville fractional derivative, \(1 < q < 2\). Some mistakes in the literature are pointed out and some new inequalities and existence and uniqueness results are obtained.
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7022469
Wikidata QID: Q59038663
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/486040
OpenAlex ID: W2044249373
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description: scientific article; zbMATH DE number 7022469