African Diaspora Journal of Mathematics

Asymptotic Behavior of Mild Solutions of Some Fractional Functional Integro-differential Equations

Giséle Mophou, Gaston M. N'Guérékata, and Vincent Valmorin

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Abstract

In this paper, we prove a new composition theorem for asymptotically antiperiodic and weighted pseudo antiperiodic functions. We also give some sufficient conditions to ensure invertibility of convolution operators in the space of antiperiodic functions. Then we prove the existence and uniqueness of asymptotically antiperiodic mild solutions to some fractional functional integro-differential equations in a Banach space using the Banach's fixed point theorem.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 16, Number 1 (2013), 70-81.

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1391091308

Mathematical Reviews number (MathSciNet)
MR3161672

Zentralblatt MATH identifier
1294.47100

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 45M05: Asymptotics

Keywords
integro-differential equation mild solution anti-periodicity

Citation

Mophou, Giséle; N'Guérékata, Gaston M.; Valmorin, Vincent. Asymptotic Behavior of Mild Solutions of Some Fractional Functional Integro-differential Equations. Afr. Diaspora J. Math. (N.S.) 16 (2013), no. 1, 70--81. https://projecteuclid.org/euclid.adjm/1391091308


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