Acta mathematica scientia, Series B >
THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
Received date: 2009-09-27
Revised date: 2010-11-20
Online published: 2011-07-20
In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type
cDδ0+u(t) = f(t, u(t), cDσ0+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 cDδ0+, cDσ0+ 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.
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 . DOI: 10.1016/S0252-9602(11)60320-2
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