A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t)+Ax(t)=f(t,xt), t∈[0,T], x(t)=ϕ(t), t∈]−∞,0], with T>0 and 0<&#x03B1...

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Main Authors: Gisle M. Mophou, Gaston M. N'Guérékata
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Advances in Difference Equations
Online Access:http://dx.doi.org/10.1155/2010/674630
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spelling doaj-0f5efada20c7401eba0a157dd7e626472020-11-24T22:19:33ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-01201010.1155/2010/674630A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite DelayGisle M. MophouGaston M. N'GuérékataWe deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t)+Ax(t)=f(t,xt), t∈[0,T], x(t)=ϕ(t), t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness) of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(t))t≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results. http://dx.doi.org/10.1155/2010/674630
collection DOAJ
language English
format Article
sources DOAJ
author Gisle M. Mophou
Gaston M. N'Guérékata
spellingShingle Gisle M. Mophou
Gaston M. N'Guérékata
A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay
Advances in Difference Equations
author_facet Gisle M. Mophou
Gaston M. N'Guérékata
author_sort Gisle M. Mophou
title A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay
title_short A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay
title_full A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay
title_fullStr A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay
title_full_unstemmed A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay
title_sort note on a semilinear fractional differential equation of neutral type with infinite delay
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1839
1687-1847
publishDate 2010-01-01
description We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t)+Ax(t)=f(t,xt), t∈[0,T], x(t)=ϕ(t), t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness) of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(t))t≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.
url http://dx.doi.org/10.1155/2010/674630
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