Monotone and concave positive solutions to a boundary value problem for higher-order fractional differential equation
type: Item
instance of: scholarly article
title: Monotone and concave positive solutions to a boundary value problem for higher-order fractional differential equation
zbMATH Open document ID: 1230.34009
DOI: 10.1155/2011/430457
author: Hongjun Xiang
author: Yuling Zhao
author: J. H. Wang
published in: Abstract and Applied Analysis
publication date: 2011-10-27T00:00:00Z
review text: Summary: We consider the boundary value problem for the nonlinear fractional differential equation \[ D^\alpha_{0+}u(t) + f(t, u(t)) = 0,\;0 < t < 1,\;n - 1 < \alpha \leq n,\;n > 3, \] \[ u(0) = u'(1) = u''(0) = \cdots = n^{(n-1)}(0) = 0, \] where \(D^\alpha_{0+}\) denotes the Caputo fractional derivative. By using a fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone and concave.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5964394
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/430457
OpenAlex ID: W2109532916
Wikidata QID: Q58654208
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description: scientific article; zbMATH DE number 5964394