MULTIPLE POSITIVE SOLUTIONS OF BVPS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-CARATHEODORY NONLINEARITIES

Yuji Liu

doi:10.3846/13926292.2014.925984

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.

Highlights

Fourth order two-point boundary value problems are useful for material mechanics because the problems usually characterize the deflection of an elastic beam
In [24], the authors studied the existence of positive solutions of the following boundary value problem (a generalization of BVP (1.1)) for the fractional order beam equation
In [18], authors studied the existence of positive solutions for fractional order elastic beam equation

Summary

Introduction

Fourth order two-point boundary value problems are useful for material mechanics because the problems usually characterize the deflection of an elastic beam. The use of cone theoretic techniques in studies of the existence of positive solutions of boundary value problems for differential equations with fractional order α ∈

Objectives

Results

Conclusion