Comparison principles for fractional differential equations with the Caputo derivatives

Abstract

Abstract In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n−1<p≤n $0\leq n-1< p\leq n$. First, we present comparison results with strict inequalities for fractional differential equations with the Caputo derivatives. Then we investigate local existence and extremal solutions for fractional differential equations with the Caputo derivatives. Finally, we consider comparison results with nonstrict inequalities for fractional differential equations with the Caputo derivatives.

Keywords

• Comparison principle
• Fractional differential equation
• Caputo derivatives
• Local existence
• Extremal solutions