Multiple Positive Solutions of BVPs for Singular Fractional Differential Equations with Non-Caratheodory Nonlinearities

Abstract

In this article, the existence of multiple positive solutions of boundary-value problems for nonlinear singular fractional order elastic beam equations is established. Here f depends on x, x′ and x″, f may be singular at t = 0 and t = 1 and f is non-Caratheodory function. The analysis relies on the well known Schauder fixed point theorem and the five functional fixed point theorems in the cones.