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

• Published in: Mathematical modelling and analysis Vol. 24; no. 1; pp. 62 - 71
• Main Authors: Al-Refai, Mohammed, Pal, Kamal
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.01.2019
• Subjects: Boundary conditions; Boundary value problems; Caputo-Fabrizio fractional derivative; Convection; Derivatives (Mathematics); Economic models; fractional differential equations; Linear differential equations; Mathematical research; Maximum principle; fractional differential equations; maximum principle; Caputo-Fabrizio fractional derivative
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2019.005

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