Positive solutions for boundary-value problems of nonlinear fractional differential equations

Zhang, Shuqin

Electronic journal of differential equations, Tome 2006 (2006)

Résumé

In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem

$\displaylines{ \hbox{\bf D}_{0+}^\alpha u(t)=f(t,u(t)),\quad 0 less than t less than 1\cr u(0)+u'(0)=0,\quad u(1)+u'(1)=0 }$

where $1 less than \alpha\leq 2$ is a real number, and $\hbox{\bf D}_{0+}^\alpha$ is the Caputo's fractional derivative, and $f:[0,1]\times[0,+\infty)\to [0,+\infty)$ is continuous. By means of a fixed-point theorem on cones, some existence and multiplicity results of positive solutions are obtained.

Détail

Classification : 34B15
Keywords: Caputo's fractional derivative, fractional differential equation, boundary-value problem, positive solution, fractional Green's function, fixed-point theorem