A maximum principle for a fractional boundary value problem with convection term and applications

Abstract

We consider a fractional boundary value problem with Caputo-Fabrizio fractional derivative of order 1 < α < 2 We prove a maximum principle for a general linear fractional boundary value problem. The proof is based on an estimate of the fractional derivative at extreme points and under certain assumption on the boundary conditions. A prior norm estimate of solutions of the linear fractional boundary value problem and a uniqueness result of the nonlinear problem have been established. Several comparison principles are derived for the linear and nonlinear fractional problems. First Published Online: 21 Nov 2018

Keywords

• fractional differential equations
• Caputo-Fabrizio fractional derivative
• maximum principle