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.
Liu, Y. (2014). Multiple Positive Solutions of BVPs for Singular Fractional Differential Equations with Non-Caratheodory Nonlinearities. Mathematical Modelling and Analysis, 19(3), 395-416. https://doi.org/10.3846/13926292.2014.925984
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