On the Existence and multiplicity of Positive Solutions for a $p$-Laplacian Fractional Boundary Value Problem with an Integral Boundary Condition

Abstract

‎The aim of this work is to investigate the existence and multiplicity of positive solutions of a kind of fractional boundary value problem with an integral boundary conditions with $p$-Laplacian operator‎. ‎By using some fixed point theorems such as‎, ‎Krasnoselskii‏,‎ ‎Schaefer‎ and Leggett-Williams fixed point theorems‎, ‎necessary and sufficient conditions are presented to obtain existence and multiplicity results‎. ‎Two examples are given to illustrate our results‎.