Existence of Two Positive Solutions for Third Order Nonlinear Fractional Differential Equations with Integral Boundary Conditions in Cone Banach Space

Abstract

In this work, we applied Avery Henderson fixed point theorem to obtain the existence of two positive solutions for third order nonlinear fractional differential equations with integral boundary conditions in cone Banach space. First, Green’s function of the corresponding linear boundary value problem is constructed. Next, some useful properties of the Green’s function are obtained. Finally, existence results of at least two positive solutions for the fractional order boundary value problem are established by imposing some suitable conditions on and An example is also included to illustrate the main results of this paper.