Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition. (28th January 2021)

• Record Type: Journal Article
• Authors: Bachar, Imed; Mâagli, Habib; Eltayeb, Hassan
• Other Names: Avery Rich Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6666015
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper deals with the following boundary value problem D α u t = f t, u t, t ∈ 0, 1, u 0 = u 1 = D α − 3 u 0 = u ′ 1 = 0, where 3 < α ≤ 4, D α is the Riemann-Liouville fractional derivative, and the nonlinearity f, which could be singular at both t = 0 and t = 1, is required to be continuous on 0, 1 × ℝ satisfying a mild Lipschitz assumption. Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution u satisfying u t ≤ c ω t, for t ∈ 0, 1 and c > 0, where ω t ≔ t α − 2 1 − t 2 .