Positive solutions of a class of nonlinear boundary value fractional differential equations

Abstract

In this paper, the existence of positive solutions of a class of nonlinear fractional boundary value problemsis considered. Two fixed point theorems are used, namely: Banach Contraction mapping principle andLeggett-Williams fixed point theorems. The former is used to prove the existence of a unique solution, whereasthe latter is used to prove the existence of at least three positive solutions to the problem. Some examples areprovided to illustrate the two results.