Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664481 | Acta Mathematica Scientia | 2011 | 10 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mujeeb ur Rehman, Rahmat Ali Khan, Naseer Ahmad Asif,