Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces

Abstract

In this article, a recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas [1998, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, 161–168] is used to investigate the existence and uniqueness of solutions for fractional order functional differential equations with infinite delay.

Keywords:

• Functional differential equations
• Fractional order
• Infinite delay
• Contraction

Keywords:

• AMS (MOS) Subject Classifications: 34K40
• 26A33
• 26A42

Acknowledgement

The authors thank the referee for his/her remarks.