On a solution to fractional order integrodifferential equations with analytic semigroups
type: Item
instance of: scholarly article
title: On a solution to fractional order integrodifferential equations with analytic semigroups
zbMATH Open document ID: 1201.45013
author: Amit Ujlayan
author: Dwijendra N. Pandey
author: Dhirendra Bahuguna
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-10T00:00:00Z
review text: The authors consider the integrodifferential equation \[ {d^\eta u(t)\over dt^\eta}+ Au(t)= f(t, u(t))+ \int^t_{t_0} a(t- s) g(s, u(s))\,ds, \] for \(t\geq t_0\), in a Banach space \(X\). Here \(-A\) is the generator of an analytic semigroup and \(\eta\in(0, 1]\). The functions \(f\), \(g\) are suitably bounded nonlinear functions and the kernel \(a\in L^1_{\text{loc}}\). Using the contraction mapping principle the existence and regularity of solutions is proved.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 5577437
zbMATH Keywords: integrodifferential equations
zbMATH Keywords: existence of solutions
reviewed by: Stig-Olof Londen
MaRDI profile type: Publication
full work available at URL: j.na.2009.02.018
OpenAlex ID: W1992368105
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DOI: 10.1016/J.NA.2009.02.018
description: scientific article; zbMATH DE number 5577437