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

    Mohammed Al-Refai Affiliation
    ; Kamal Pal Affiliation

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

Keyword : fractional differential equations, Caputo-Fabrizio fractional derivative, maximum principle

How to Cite
Al-Refai, M., & Pal, K. (2019). A maximum principle for a fractional boundary value problem with convection term and applications. Mathematical Modelling and Analysis, 24(1), 62-71. https://doi.org/10.3846/mma.2019.005
Published in Issue
Jan 1, 2019
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This work is licensed under a Creative Commons Attribution 4.0 International License.