Existence and Multiplicity of Positive Solutions for a Singular Nonlinear High Order Fractional Differential Problem with Multi-Point Boundary Conditions

Abstract

In this paper, a singular nonlinear high order fractional differential problem involving multi-point boundary conditions is solved by means of the fixed point index theory. Some properties of the first eigenvalue corresponding to relevant operator and some new height functions are also used to prove the existence and multiplicity of positive solutions. The nonlinearity depends on arbitrary fractional derivative.