Extremal Solutions for a Caputo-Type Fractional-Order Initial Value Problem

Abstract

In this paper, we study the existence of extremal solutions for a Caputo-type fractional-order initial value problem. By using the monotone iteration technique and the upper–lower solution method, we obtain our existence theorem when the nonlinearity satisfies a reverse-type Lipschitz condition. Note that our nonlinearity depends on the unknown function and its fractional-order derivative.

Keywords

• Caputo-type fractional-order differential equations
• initial value problems
• extremal solutions
• upper–lower solution methods