THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(11)60320-2

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1337-1346.doi: 10.1016/S0252-9602(11)60320-2

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

Mujeeb ur Rehman¹, Rahmat Ali Khan², Naseer Ahmad Asif²

1. National University of Sciences and Technology (NUST), Centre for Advanced Mathematics and Physics, Sector H-12 Islamabad, Pakistan;
2. University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhawa, Pakistan

收稿日期:2009-09-27 修回日期:2010-11-20 出版日期:2011-07-20 发布日期:2011-07-20

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

Mujeeb ur Rehman¹, Rahmat Ali Khan², Naseer Ahmad Asif²

1. National University of Sciences and Technology (NUST), Centre for Advanced Mathematics and Physics, Sector H-12 Islamabad, Pakistan;
2. University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhawa, Pakistan

Received:2009-09-27 Revised:2010-11-20 Online:2011-07-20 Published:2011-07-20

摘要/Abstract

摘要：

In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type
^cD^δ₀+u(t) = f(t, u(t), ^cD^σ₀+u(t)), t ∈ [0, T],
u(0) = ∂u(η), u(T) = βu(η),
where 1 < δ < 2, 0 < σ < 1, α, β∈ R, η ∈ (0, T), αη(1 −β ) + (1 − α)(T − βη) ≠ 0 and ^cD^δ₀+, ^cD^σ₀+ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples
are also included to show the applicability of our results.

关键词: fractional differential equations, three point boundary conditions, existence and uniqueness results

Abstract:

Key words: fractional differential equations, three point boundary conditions, existence and uniqueness results

中图分类号:

34A08

Mujeeb ur Rehman, Rahmat Ali Khan, Naseer Ahmad Asif. THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2011, 31(4): 1337-1346.

Mujeeb ur Rehman, Rahmat Ali Khan, Naseer Ahmad Asif. THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2011, 31(4): 1337-1346.

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THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

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