Fractional Differential Equations with Nonlocal Integral and Integer-Fractional-Order Neumann Type Boundary Conditions

被引：15

作者：

Ahmad, Bashir ^{[1
]}

Ntouyas, Sotiris K. ^{[1
,2
]}

Tariboon, Jessada ^{[3
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Fac Sci, NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

[2] Univ Ioannina, Dept Math, Ioannina 45110, Greece

[3] King Mongkuts Univ Technol North Bangkok, Nonlinear Dynam Anal Res Ctr, Fac Sci Appl, Dept Math, Bangkok 10800, Thailand

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2016年 / 13卷 / 05期

关键词：

Fractional differential systems; nonlocal boundary conditions; integral boundary conditions; fixed point theorem; COUPLED SYSTEM; EXISTENCE;

D O I：

10.1007/s00009-015-0629-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a new concept of the coupling of nonlocal integral and integer-fractional-order Neumann type boundary conditions, and discuss the existence and uniqueness of solutions for a coupled system of fractional differential equations supplemented with these conditions. The existence of solutions is derived from Leray-Schauder's alternative and Schauder's fixed point theorem, while the uniqueness of solutions is established by means of Banach's contraction mapping principle. The results obtained in this paper are well illustrated with the aid of examples.

引用

页码：2365 / 2381

页数：17

共 27 条

[21] Fractional kinetics [J].

Sokolov, IM ;

Klafter, J ;

Blumen, A .

PHYSICS TODAY, 2002, 55 (11) :48-54

[22] Boundary value problem for a coupled system of nonlinear fractional differential equations [J].

Su, Xinwei .

APPLIED MATHEMATICS LETTERS, 2009, 22 (01) :64-69

[23] Existence of solutions for fractional differential systems with antiperiodic boundary conditions [J].

Sun, Jihua ;

Liu, Yiliang ;

Liu, Guifang .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (06) :1557-1566

[24] Nonlocal Hadamard fractional integral conditions for nonlinear Riemann-Liouville fractional differential equations [J].

Tariboon, Jessada ;

Ntouyas, Sotiris K. ;

Sudsutad, Weerawat .

BOUNDARY VALUE PROBLEMS, 2014,

[25] Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative [J].

Wei, Zhongli ;

Li, Qingdong ;

Che, Junling .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 367 (01) :260-272

[26] Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation [J].

Yang, Xiao-Jun ;

Hristov, Jordan ;

Srivastava, H. M. ;

Ahmad, Bashir .

ABSTRACT AND APPLIED ANALYSIS, 2014,

[27] SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ON A HALF-LINE [J].

Zhang, Lihong ;

Ahmad, Bashir ;

Wang, Guotao .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 91 (01) :116-128

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