THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

• Published in: Acta mathematica scientia Vol. 31; no. 4; pp. 1337 - 1346
• Main Authors: ur Rehman, Mujeeb, Khan, Rahmat Ali, Asif, Naseer Ahmad
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2011; National University of Sciences and Technology(NUST),Centre for Advanced Mathematics and Physics, Sector H-12 Islamabad, Pakistan%University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhawa, Pakistan
• Subjects: 34A08; Boundary value problems; Derivatives; Differential equations; existence and uniqueness results; fractional differential equations; Mapping; Mathematical analysis; Nonlinearity; Schauder不动点定理; three point boundary conditions; Uniqueness; 分数微分方程; 压缩映射原理; 衍生物; 解的存在性; 边界值问题; 适用性; 非线性三点边值问题; three point boundary conditions; fractional differential equations; existence and uniqueness results; 34A08
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(11)60320-2

In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0＋ u（t） = f （t, u（t）, c D σ 0＋ u（t））, t ∈ [0, T ], u（0） = αu（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 c D δ 0＋ , c D σ 0＋ 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.