On the Existence of Solutions for Nonlinear Boundary Value Problems
Project no. 659 · Status: Kapanmış · 2015
Summary
This project consists of four main chapters including the introduction part. In the second chapter, basic definitions and theorems about the fractional derivative and fixed point theory are introduced, which will be used throughout this work. In the third chapter, the Green’ s functions corresponding to the homogeneous boundary value problems are constructed and the bounds for the Green’s functions are determined. First, using the Bai and Ge’ s fixed point theorem, the existence of at least three positive solutions to the boundary value problems for a nonlinear fractional differential system is established. Besides, an example is given to support our main result. Then, existence of at least one and two positive solutions is investigated by using the Krasnoselskii fixed point theorem. In the fourth chapter, the results obtained from our study are represented.