Non-negative Solutions to the Nonlinear Fractional Boundary Value Problem

This paper investigates the possibility of having a number of positive solutions for the type of nonlinear fractional differential equations. There are certain boundary conditions applied to this equation. The main objective is to identify the conditions that allow for the existence of these multiple positive solutions. In order to attain this, we use Avery-Peterson’s fixed-point theorem and Schauder’s fixed point theorem, obtaining sufficient condition for the solutions. In order to improve clarity, the article offers examples and demonstrations that support its conclusions. To simplify it briefly, the article uses fixed-point theorems (FPTs) to define the criteria necessary for the existence of multiple positive solutions in the nonlinear fractional differential equations under consideration, together with the corresponding boundary conditions.