Existence of solutions for Riemann-Liouville fractional boundary value problem. (English) Zbl 1474.34152

Xie, Wenzhe; Xiao, Jing; Luo, Zhiguo

Abstr. Appl. Anal. 2014, Article ID 540351, 9 p. (2014).

Summary: By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann-Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in [M. Al-Refai, Electron. J. Qual. Theory Differ. Equ. 2012, Paper No. 55, 5 p. (2012; Zbl 1340.26009)]. As applications, an example is presented to illustrate our main results.

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34A08	Fractional ordinary differential equations

Citations:

Zbl 1340.26009

References:

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