Article ID Journal Published Year Pages File Type
4664481 Acta Mathematica Scientia 2011 10 Pages PDF
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 Dδ0+cu(t) = f(t,u(t), Dσ0+cu(t)), t ∈ [0, T],u(0) = αu(η), u(T) = βu(η),where 1 < δ < 2, 0 < σ < 1, α < 1, α, β ∈ ℝ, η ∈ (0,T), αη(1 − β) + (1 − α) (T − βη) ≠ 01 < δ < 2, 0 < σ < 1, α < 1, α, β ∈ ℝ, η ∈ (0,T), αη(1 − β) + (1 − α) (T − βη) ≠ 0 and Dcδ0+,Dcσ0+ 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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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