Pseudo asymptotic solutions of fractional order semilinear equations
type: Item
instance of: scholarly article
title: Pseudo asymptotic solutions of fractional order semilinear equations
zbMATH Open document ID: 1275.47092
author: Carlos Lizama
author: Edgardo Alvarez-Pardo
published in: Banach Journal of Mathematical Analysis
publication date: 2013-03-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bjma/1363784222
review text: In this paper, the authors study the fractional order differential equation \[ D^{\alpha+1}_tu(t)+\mu D^\beta_tu(t)-Au(t)=f(t,u(t))\,, \qquad t>0, \] with prescribed initial conditions \(u(0)\) and \(u'(0)\). Here, \(A:D(A)\subset X \to X\) is a sectorial operator, \(f\) is a vector-valued function, \(\alpha\) and \(\beta\) are two parameters such that \(0<\alpha\leq \beta\leq 1\), \(\mu\geq 0\), and \(D^\gamma_t\) denotes the Caputo fractional derivative of order \(\gamma\). In the main results of the paper, the authors prove the existence and uniqueness of solutions for this problem, using the contraction mapping theorem.
reviewed by: Raffaella Servadei
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 45N05
zbMATH DE Number: 6147458
zbMATH Keywords: Caputo derivative
zbMATH Keywords: fractional order differential equations
zbMATH Keywords: generalized semigroup theory
zbMATH Keywords: two-term time fractional derivative
zbMATH Keywords: sectorial operators
zbMATH Keywords: pseudo asymptotic solutions
MaRDI profile type: Publication
OpenAlex ID: W1989404666
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DOI: 10.15352/BJMA/1363784222
description: scientific article; zbMATH DE number 6147458