Existence results of positive solutions for boundary value problems of fractional differential equations

• Published in: Boundary value problems Vol. 2013; no. 1; p. 109
• Main Author: Chai, Guoqing
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 29.04.2013; BioMed Central Ltd
• Subjects: Analysis; Approximations and Expansions; Difference and Functional Equations; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; positive solution; fractional differential equations; existence results; fixed point theorem
• ISSN: 1687-2770; 1687-2770
• DOI: 10.1186/1687-2770-2013-109

In this paper, we are concerned with the following fractional equation: D 0 + α C u ( t ) = f ( t , u ( t ) , u ′ ( t ) ) , t ∈ ( 0 , 1 ) with the boundary value conditions u ( 1 ) = u ′ ( 1 ) = 0 , δ u ″ ( 0 ) = u ″ ( 1 ) , γ u ‴ ( 0 ) = u ‴ ( 1 ) , where D 0 + α C is the standard Caputo derivative with 3 < α ≤ 4 and δ , γ are constants with δ > 1 , γ > 1 . By applying a new fixed point theorem on cone and Krasnoselskii’s fixed point theorem, some existence results of positive solution are obtained. MSC: 34A08, 34B15, 34B18.