Positive Solutions For BVP Of Nonlinear Fractional Differential Equation

Fractional differential equations arise from a variety of different areas of science and engineering, e.g., in the signal and image processing, blood flow phenomena, fitting of experimental, etc. Recently, the boundary value problems (BVPs for short) of nonlinear fractional differential equations have received much attention from many authors.In this paper, we consider the following BVP of nonlinear fractional differential equation where α∈ (2,3], cDα0+ denotes the standard Caputo fractional derivative and f∈ C([0,1]× [0,+∞),[0,+∞)).In chapter 2 and chapter 3, we obtain the existence of single and multiple posi-tive solutions for the above problem. The main tools used are the Guo-Krasnoselskii and Leggett-Williams fixed point theorems. In chapter 4, by constructing a itera-tive sequence and using the iterative technique, we obtain the existence of monotone positive solution for the above problem.