Positive solutions for integral boundary value problem of two-term fractional differential equations

Abstract

Abstract In this paper, we investigate a class of nonlinear two-term fractional differential equations involving two fractional orders δ∈(1,2] $\delta\in(1,2]$ and τ∈(0,δ) $\tau\in (0,\delta)$ with integral boundary value conditions. By the Schauder fixed point theorem we obtain the existence of positive solutions based on the method of upper and lower solutions. Then we obtain the uniqueness result by the Banach contraction mapping principle. Examples are given to illustrate our main results.

Keywords

• Fractional differential equations
• Boundary value problem
• Positive solutions