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

Mohammed Al-Refai; Kamal Pal

doi:10.3846/mma.2019.005

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

Mohammed Al-Refai, Kamal Pal

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

We onsider a frational boundary value problem with Caputo-Fabrizio frational derivative of order 1 < α < 2. We prove a maximum priniple for a general linear frational boundary value problem. The proof is based on an estimate of the frational derivative at extreme points and under ertain assumption on the boundary onditions. A prior norm estimate of solutions of the linear frational boundary value problem and a uniqueness result of the nonlinear problem have been established. Several omparison priniples are derived for the linear and nonlinear frational problems.

Original language	English
Pages (from-to)	62-71
Number of pages	10
Journal	Mathematical Modelling and Analysis
Volume	24
Issue number	1
DOIs	https://doi.org/10.3846/mma.2019.005
Publication status	Published - Nov 21 2019

Keywords

Caputo-fabrizio fractional derivative
Fractional differential equations
Maximum principle

ASJC Scopus subject areas

Analysis
Modelling and Simulation

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10.3846/mma.2019.005

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title = "A maximum principle for a fractional boundary value problem with convection term and applications",

abstract = "We onsider a frational boundary value problem with Caputo-Fabrizio frational derivative of order 1 < α < 2. We prove a maximum priniple for a general linear frational boundary value problem. The proof is based on an estimate of the frational derivative at extreme points and under ertain assumption on the boundary onditions. A prior norm estimate of solutions of the linear frational boundary value problem and a uniqueness result of the nonlinear problem have been established. Several omparison priniples are derived for the linear and nonlinear frational problems.",

keywords = "Caputo-fabrizio fractional derivative, Fractional differential equations, Maximum principle",

author = "Mohammed Al-Refai and Kamal Pal",

note = "Funding Information: The authors acknowledge the support of the United Arab emirates University under the Fund No. 31S239-UPAR(1) 2016. Publisher Copyright: {\textcopyright} 2019 The Author(s).",

year = "2019",

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day = "21",

doi = "10.3846/mma.2019.005",

language = "English",

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pages = "62--71",

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TY - JOUR

T1 - A maximum principle for a fractional boundary value problem with convection term and applications

AU - Al-Refai, Mohammed

AU - Pal, Kamal

PY - 2019/11/21

Y1 - 2019/11/21

N2 - We onsider a frational boundary value problem with Caputo-Fabrizio frational derivative of order 1 < α < 2. We prove a maximum priniple for a general linear frational boundary value problem. The proof is based on an estimate of the frational derivative at extreme points and under ertain assumption on the boundary onditions. A prior norm estimate of solutions of the linear frational boundary value problem and a uniqueness result of the nonlinear problem have been established. Several omparison priniples are derived for the linear and nonlinear frational problems.

AB - We onsider a frational boundary value problem with Caputo-Fabrizio frational derivative of order 1 < α < 2. We prove a maximum priniple for a general linear frational boundary value problem. The proof is based on an estimate of the frational derivative at extreme points and under ertain assumption on the boundary onditions. A prior norm estimate of solutions of the linear frational boundary value problem and a uniqueness result of the nonlinear problem have been established. Several omparison priniples are derived for the linear and nonlinear frational problems.

KW - Caputo-fabrizio fractional derivative

KW - Fractional differential equations

KW - Maximum principle

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EP - 71

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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