Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation

YANG Jun; LIU Dongli; ZHANG Bo

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Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation

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- Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 1, Pages: 34-41(2014)
- 作者机构：
  
  1. 燕山大学理学院,河北,秦皇岛,066004
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 January 2014，
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YANG Jun, LIU Dongli, ZHANG Bo. Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(1):34-41(2014)
DOI：

YANG Jun, LIU Dongli, ZHANG Bo. Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(1):34-41(2014) DOI：

摘要

研究了以下一类拟线性分数阶高阶脉冲微分方程边值问题D

y(t) = A(t

y)y(t)+f(t

y(t)

Φy(t)

Ψy(t))

t∈［0

1］

q∈(n－1

y(i)(0)=0

Δy(i) |

t=tk

= 0

1≤i≤n－2

k=1

…

Δy |

t=tk

= I

(y(t

))

Δy

(n－1)

t=tk

= J

(y(t

))

k=1

…

y(0) = y

+ g(y)

(n－1)

(1) = y1+∑

m－2

j=1

(n－1)

(ξ

) 解的存在性。通过定义一个压缩映射并利用Banach不动点定理和Krasnoselskiis不动点定理，得到了边值问题存在唯一解和至少存在一个解的充分条件，最后分别给出一个例子来验证主要结果。

Abstract

The existence of solutions for high-order impulsive boundary value problem of Caputo fractional differential equation in the formD

y(t) = A(t

y)y(t)+f(t

y(t)

Φy(t)

Ψy(t))

t∈［0

1］

q∈(n－1

y(i)(0)=0

Δy(i) |

t=tk

= 0

1≤i≤n－2

k=1

…

Δy |

t=tk

= I

(y(t

))

Δy

(n－1)

t=tk

= J

(y(t

))

k=1

…

y(0) = y

+ g(y)

(n－1)

(1) = y1+∑

m－2

j=1

(n－1)

(ξ

) is studied. By defining a contraction mapping and using the fixed point theorems

some sufficient conditions for the existence of one unique solution and at least a solution are established. Further

two examples are presented to illustrate the main results respectively.

关键词

分数阶微分方程高阶脉冲Caputo分数阶导数不动点定理

Keywords

fractional differential equationshigh-orderimpulsiveCaputo fractional derivativefixed point theorems

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

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Related Institution

College of Mathematics, Zhengzhou University of Aeronautics

．南京理工大学理学院

 2．苏州科技学院土木工程学院

School of Mathematics and Statistics, Hanshan Normal College

Faculty of Information Technology, Macao University of Science and Technology, Macao

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