Existence of solutions for fractional differential equation with periodic boundary condition

Abstract

We investigate the existence of solutions for a Caputo fractional differential equation with periodic boundary condition. Using the positivity of Green's function of the corresponding linear equation, we show the existence of positive solutions by using Krasnosel'skii fixed point theorem. Meanwhile, by using monotone iterative method and lower and upper solutions method, we also discuss the existence of extremal solutions for a special case.

Keywords

• caputo fractional differential equation
• periodic boundary condition
• krasnosel'skii fixed point theorem
• monotone iterative method
• green's function