Positive solutions of fractional differential equations with the Riesz space derivative. (September 2019)

• Record Type: Journal Article
• Authors: Gu, Chuan-Yun; Zhang, Jun; Wu, Guo-Cheng
• Is Part Of: Applied mathematics letters. Volume 95(2019)
• Page Start: 59
• Page End: 64
• Publication Date: 2019-09
• Subjects: Positive solution -- Fractional differential equation -- Riesz–Caputo derivative -- Boundary value problem; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.03.006
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: A new class of fractional differential equations with the Riesz–Caputo derivative is proposed and the physical meaning is introduced in this paper. The boundary value problem is investigated under some conditions. Leray–Schauder and Krasnoselskii's fixed point theorems in a cone are adopted. Existence of positive solutions is provided. Finally, two examples with numerical solutions are given to support theoretical results.