Polynomial decay of mild solutions to semilinear fractional differential equations with nonlocal initial conditions
type: Item
instance of: scholarly article
title: Polynomial decay of mild solutions to semilinear fractional differential equations with nonlocal initial conditions
zbMATH Open document ID: 1493.34027
author: Do Van Loi
author: Hoang Nam
author: Vu Trong Luong
published in: Differential Equations and Dynamical Systems
publication date: 2021-04-23T00:00:00Z
review text: This paper deals with the following fractional differential equation \[ \begin{aligned} &D_{0}^{\alpha-1}u(t) + \mu D_{0}^{\beta}u(t) - Au(t) = F(t,u(t)), \quad t>0, \mu \geq 0,\\ &u(0) + g(u) = u_0, \quad u_t(0) = 0, \end{aligned}\tag{1} \] where \(0< \alpha \leq \beta \leq 1\), \(D_{0}^{\alpha}\) is the Caputo fractional derivative, \(A: D(A)\subset X \to X\) is a closed linear operator and \(u_0\in X\). By using a fixed point principle for condensing maps for measures of noncompactness and the theory of \((\alpha, \beta)\)-regularized families the authors prove the existence of decay of mild solutions with \[ \|u(t)\| = O(t^{-\gamma}) \;\;\mbox{as}\;\;t\to \infty. \]
reviewed by: César Torres
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 7336975
zbMATH Keywords: decay rate of mild solutions
zbMATH Keywords: fractional differential equations
zbMATH Keywords: nonlocal conditions
zbMATH Keywords: measure of noncompactness
MaRDI profile type: Publication
full work available at URL: s12591-018-0419-5
OpenAlex ID: W2800030348
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Wikidata QID: Q129979673
DOI: 10.1007/S12591-018-0419-5
description: scientific article; zbMATH DE number 7336975