Positive solutions for superlinear Riemann-Liouville fractional boundary-value problems

Abstract

Using a perturbation argument, we establish the existence and uniqueness of a positive continuous solution for the following superlinear Riemann-Liouville fractional boundary-value problem $$\displaylines{ D^{\alpha }u( x) -u(x)\varphi (x,u(x))=0,\quad 00, }$$ where $3<\alpha \leq 4$ and $\varphi (x,t)$ satisfies a suitable integrability condition.

Keywords

• Fractional differential equation
• positive solution
• Green's function
• perturbation
• Schauder fixed point theorem