new approach to the study of solutions for a fractional boundary value problem in Holder spaces

In this paper, we study the existence of nontrivial solutionsfor a fractional boundary value problem in Holder spaces by a technicalapproach based on Leray-Schauder nonlinear alternative. Moreover,using the concept of orthogonal set on Banach xed point theorem weobtain another existence result with weaker conditions. Also, recentresults are extended and improved. In addition, we give some examplesto illustrate the feasibility and eectiveness of our results.