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

• Main Authors: N'Guérékata GastonM, Mophou GisleM
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2010/674630

<p/> <p>We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: <inline-formula><graphic file="1687-1847-2010-674630-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-674630-i2.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-674630-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-674630-i4.gif"/></inline-formula>, with <inline-formula><graphic file="1687-1847-2010-674630-i5.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-674630-i6.gif"/></inline-formula>. We prove the existence (and uniqueness) of solutions, assuming that <inline-formula><graphic file="1687-1847-2010-674630-i7.gif"/></inline-formula> is a linear closed operator which generates an analytic semigroup <inline-formula><graphic file="1687-1847-2010-674630-i8.gif"/></inline-formula> on a Banach space <inline-formula><graphic file="1687-1847-2010-674630-i9.gif"/></inline-formula> by means of the Banach's fixed point theorem. This generalizes some recent results.</p>