Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument

Abstract

Abstract In this article, we consider the existence of at least one positive solution to the three-point boundary value problem for nonlinear fractional-order differential equation with an advanced argument where 2 < α ≤ 3, 0 < η < 1, , CDα is the Caputo fractional derivative. Using the well-known Guo-Krasnoselskii fixed point theorem, sufficient conditions for the existence of at least one positive solution are established. MSC (2010): 34A08; 34B18; 34K37.

Keywords

• Positive solution
• Three-point boundary value problem
• Fractional differential equations
• Guo-Krasnoselskii fixed point theorem
• Cone