THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

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

Abstract

Abstract:

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.

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

CLC Number:

34A08

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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