New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions. (27th April 2020)

• Record Type: Journal Article
• Authors: Zhang, Haiyan; Li, Yaohong; Yang, Jingbao
• Other Names: Zhang Xinguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-04-27
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/6821637
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions C D q + k C D q − 1 u t = f t, u t, C D q − 1 u t, t ∈ 0, 1, α 1 u 0 + β 1 u 1 + γ 1 I r u η = ε 1, η ∈ 0, 1, α 2 u ′ 0 + β 2 u ′ 1 + γ 2 I r u ′ η = ε 2, where q ∈ 1, 2 is a real number, k, r > 0, α i, β i, γ i, ε i ∈ ℝ, i = 1, 2, C D q is the Caputo fractional derivative, and the boundary conditions include antiperiodic and Riemann-Liouville fractional integral boundary value cases. Our approach to treat the above problem is based upon standard tools of fixed point theory and some new inequalities of norm form. Some existence results are obtained and well illustrated through the aid of examples.