﻿ Banach空间中分数阶微分方程边值问题的解 The Solution of Boundary Value Problems for Fractional Differential Equations in Banach Spaces

Pure Mathematics
Vol.07 No.02(2017), Article ID:20028,11 pages
10.12677/PM.2017.72012

The Solution of Boundary Value Problems for Fractional Differential Equations in Banach Spaces

Jiahao Wei

Weifang (Shanghai) New Epoch School, Weifang Shandong

Received: Mar. 10th, 2017; accepted: Mar. 27th, 2017; published: Mar. 30th, 2017

ABSTRACT

The existence of solutions for a class of P-Laplacian fractional differential equation boundary value problem is obtained by means of fixed point theorem and the properties of Green function in Banach Space.

Keywords:Fractional Differential Equation, Boundary Value Problem, Fixed Point Theorem, P-Laplacian Operator

Banach空间中分数阶微分方程边值 问题的解

1. 引言

(1)

. (2)

2010年，文献 [5] 研究了下列带有P-Laplacian算子的分数阶微分方程边值问题：

2013年，文献 [6] 研究了下列带有P-Laplacian算子的分数阶微分方程边值问题：

2. 预备知识及主要引理

,

.

,

1) 如果存在常数，对E中的任意有界集S，使得，则称A是k-集压缩映像。当时，则称A为严格集压缩映像。

2) 如果对E中任意非相对紧的有界集S，有，则称A是凝聚映像。

(H1) 存在非负函数，使得对任意，有

,

;

(H2)对任意上是一致连续的，其中

;

(H3) 存在满足，使得对任意，E中的有界子集，有

,

,

.

(3)

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, (5)

,

.

, (6)

. (7)

. (8)

. (9)

. (10)

. (11)

.(12)

,

.

. (13)

. (14)

. (15)

, (16)

. (17)

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,

a) 对任意，存在，使得对任意，当时，有

;

b) 对任意，存在，使得对任意，当时，有

.

.

.

,

.

.

.

3. 主要结果

.

.

. (19)

.

, (20)

. (21)

.

4. 结论

The Solution of Boundary Value Problems for Fractional Differential Equations in Banach Spaces[J]. 理论数学, 2017, 07(02): 78-88. http://dx.doi.org/10.12677/PM.2017.72012

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