Caputo-Fabrizio型分数阶微分方程两点边值问题正解的存在性

doi:10.13438/j.cnki.jdzk.2023.05.001

吉首大学学报（自然科学版） ›› 2023, Vol. 44 ›› Issue (5): 1-5.DOI: 10.13438/j.cnki.jdzk.2023.05.001

• 数学 • 下一篇

Caputo-Fabrizio型分数阶微分方程两点边值问题正解的存在性

王兰芳

（吉首大学数学与统计学院，湖南吉首 416000）

出版日期:2023-09-25 发布日期:2023-11-21
作者简介:王兰芳(1964—)，女，湖南醴陵人，吉首大学数学与统计学院副教授，主要从事微分方程研究.

Existence of Positive Solutions to Two-Point Boundary Value Problems of Fractional Differentional Equations Involving Caputo-Fabrizio Fractional Derivatives

WANG Lanfang

（College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China）

Online:2023-09-25 Published:2023-11-21

摘要/Abstract

摘要：利用Krasnoselskii不动点定理，讨论了一类含高阶Caputo-Fabrizio型分数阶导数的分数阶微分方程两点边值问题正解的存在性，建立了该边值问题至少存在1个正解的充分条件.

关键词： 分数阶微分方程, Caputo-Fabrizio导数, 边值问题, 正解, 不动点定理

Abstract: Based on the Krasnoselskii fixed point theorem，existence of positive solutions to two-point boundary value problems for fractional differential equations involving the Caputo-Fabrizio derivative is discussed，and some sufficient conditions are established to ensure the existence of at least one positive solutions to the boundary problem.

Key words: fractional differential equations, Caputo-Fabrizio derivatives, boundary value problems, positive solutions, fixed points

王兰芳. Caputo-Fabrizio型分数阶微分方程两点边值问题正解的存在性[J]. 吉首大学学报（自然科学版）, 2023, 44(5): 1-5.

WANG Lanfang. Existence of Positive Solutions to Two-Point Boundary Value Problems of Fractional Differentional Equations Involving Caputo-Fabrizio Fractional Derivatives[J]. Journal of Jishou University(Natural Sciences Edition), 2023, 44(5): 1-5.

参考文献

[1] KILBAS A A A,SRIVASTAVA HARI MOHAN,TRUJILLO JUAN J.Theory and Applications of Fractional Differential Equations[M]∥North-Hollan Mathematics Studies.Amsterdam:Elsevier Science B.V.,2006.
[2] STANISLAVSKY A,WERON K.Two-Time Scale Subordination in Physical Processes with Long-Term Memory[J].Annals of Physics,2008,323(3):643-653.
[3] HARKO TIBERIU,LEUNG CHUN SING,MOCANU GABRIELA.Generalized Langevin Equation with Colored Noise Description of the Stochastic Oscillations of Accretion Disks[J].European Physical Journal C,2014,74:2900.
[4] CAPUTO MICHELE,FABRIZIO MAURO.A New Definition of Fractional Derivative Without Singular Kernel[J].Progress in Fractional Differentiation and Applications,2015,2:73-75.
[5] ATANGANA ABDON,BALEANU DUMITRU.New Fractional Derivatives with Nonlocal and Non-Singular Kernel:Theory and Application to Heat Transfer Model[J].Thermal Science,2016,20(2):763-769.
[6] NISAR KOTTAKKARAN SOOPPY,FARMAN MUHAMMAD,HINCAL EVREN,et al.Modelling and Analysis of Bad Impact of Smoking in Society with Constant Proportional-Caputo Fabrizio Operator[J].Chaos,Soliton & Fractals,2023,172:113549.DOI:10.1016/j.chaos.2023.113549.
[7] NGUYEN H T,NGUYEN A T,NGUYEN HUU H C.Existence and Continuity Results for Kirchhoff Parabolic Equation with Caputo-Fabrizio Operator[J].Chaos,Soliton & Fractals,2023,167:113028.DOI:10.1016/j.chaos.2022.113028.
[8] ZHONG Wenyong,WANG Lanfang,ABDELJAWAD THABET.Separation and Stability of Solutions to Nonlinear Systems Involving Caputo-Fabrizio Derivatives[J].Advances in Difference Equations,2020,2020:166.
[9] RAVICHANDRAN C,LOGESWARI K,GMEZ-AGUILAR J F.An Epidemiological Model for Computer Virus with Atangana-Baleanu Fractional Derivative[J].Results in Physics,2023,8:1-8.
[10] ABDELJAWAD THABET.Fractional Operators with Exponential Kernels and a Lyapunov Type Inequality[J].Advances in Difference Equations,2017,2017:313.
[11] ABDELJAWAD THABET.A Lyapunov Type Inequality for Fractional Operators with Nonsingular Mittag-Leffler Kernel[J].Journal of Inequalities and Applications,2017(1):130.
[12] KRASNOSEL' SKII M A.Positive Solutions of Operator Equations[M].Groningen:P.Noordhof Ltd.,1964:135-137.

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[15]	李楚玲, 许绍元. 连续函数的Altman型不动点定理[J]. journal6, 2014, 35(5): 6-9.

Caputo-Fabrizio型分数阶微分方程两点边值问题正解的存在性

Existence of Positive Solutions to Two-Point Boundary Value Problems of Fractional Differentional Equations Involving Caputo-Fabrizio Fractional Derivatives

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