Existence and uniqueness of positive solutions to higher-order nonlinear fractional differential equation with integral boundary conditions

Zhou, Chenxing

Electronic Journal of Differential Equations, Tome 2012 (2012).

Résumé

Summary: In this article, we consider the nonlinear fractional order three-point boundary-value problem $$\displaylines{ D_{0+}^{\alpha} u(t) + f(t,u(t))=0, \quad 0 t 1,\cr u(0) = u'(0) = \dots = u^{(n-2)}(0)=0, \quad u^{(n-2)}(1) = \int_0^\eta u(s)ds, }$$ where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative, $n-1 \alpha \leq n, n \geq 3$. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.

Détail

Classification : 26A33, 34B18, 34B27
Keywords: partially ordered sets, fixed-point theorem, positive solution