Existence and Uniqueness Results to a Coupled System of Fractional Order Boundary Value Problems by Topological Degree Theory. (2nd July 2016)

• Record Type: Journal Article
• Authors: Shah, Kamal; Khan, Rahmat Ali
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 7(2016)
• Page Start: 887
• Page End: 899
• Publication Date: 2016-07-02
• Subjects: Boundary conditions -- coupled system -- existence and uniqueness results -- fractional differential equations -- topological degree theory; 47J05 -- 92D25 -- 34A08 -- 34A34 -- 34K15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1177547
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study existence and uniqueness results for a coupled system of nonlinear fractional order differential subject to nonlinear more general four-point boundary condition of the following type where 0 < α, β ≤ 1 and f, g ∈ C ([0, 1] × ℝ 2, ℝ) are continuous and the nonlocal functions ϕ, ψ: ( I, ℝ) → ℝ are also continuous. The parameters η, ξ satisfy 0 < η < 1, 0 < ξ < 1, and λ i, γ i, μ i ( i = 1, 2) are real numbers. Some new existence and uniqueness results are developed for the coupled system using topological degree theory and some standard fixed point theorems. An example is also provided to illustrate our main result.