EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

doi:10.1016/S0252-9602(06)60044-1

数学物理学报(英文版)

EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

张淑琴

中国矿业大学数学系, 北京 100083

收稿日期:2003-05-26 修回日期:2003-11-07 出版日期:2006-04-20 发布日期:2006-04-20
通讯作者: 张淑琴
基金资助:
Supported by the National 973-Project from MOST and Trans-Century Training Programme Foundation for the Talents by Ministry of Education and the Postdoctoral Foundation of China.

EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

Zhang Shuqin

Department of Mathematics, China University of Mining and Technology, Beijing 100083, China

Received:2003-05-26 Revised:2003-11-07 Online:2006-04-20 Published:2006-04-20
Contact: Zhang Shuqin

摘要/Abstract

摘要：

This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative

{\begin{cases} _{0}^{C} D_{t}^{δ} u (t) = g (t, u (t)), 0 u (0) = α \neq 0, u (1) = β \neq 0. \end{cases}

$\left\{ \begin {array}{l} _0^{C}D_t^\delta u(t) =g(t,u(t)),\quad 0u(0)=\alpha\neq 0,\quad u(1)=\beta\neq 0. \end{array} \right.$

关键词: Boundary value, Laplace transform, Mittage-Leffler function, fractional derivative, Caputo's derivative, fixed point, cone

Abstract:

This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo's derivative

{\begin{cases} _{0}^{C} D_{t}^{δ} u (t) = g (t, u (t)), 0 u (0) = α \neq 0, u (1) = β \neq 0. \end{cases}

$\left\{ \begin {array}{l} _0^{C}D_t^\delta u(t) =g(t,u(t)),\quad 0u(0)=\alpha\neq 0,\quad u(1)=\beta\neq 0. \end{array} \right.$

Key words: Boundary value, Laplace transform, Mittage-Leffler function, fractional derivative, Caputo's derivative, fixed point, cone

中图分类号:

34B15

张淑琴. EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER[J]. 数学物理学报(英文版), 2006, 26(2): 220-228.

Zhang Shuqin. EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER[J]. Acta mathematica scientia,Series B, 2006, 26(2): 220-228.

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EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

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