Anti-periodic boundary value problems for Caputo-Fabrizio fractional impulsive differential equations

Abstract

In this paper, we shall discuss the existence and uniqueness of solutions for a nonlinear anti-periodic boundary value problem for fractional impulsive differential equations involving a Caputo-Fabrizio fractional derivative of order r ∈ (0, 1). Our results are based on some fixed point theorem, nonlinear alternative of Leray-Schauder type and coupled lower and upper solutions.

Keywords

• fractional differential equation
• caputo-fabrizio integral of fractional order
• caputo-fabrizio fractional derivatives
• anti-periodic boundary value problem
• fixed point
• lower and upper solutions
• coupled lower and upper solutions