Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives

Our aim in this paper is to explore the existence of nonnegative solutions for a boundary value problem involving nonlinear Caputo fractional differential equations. The analysis begins with the formulation of superlinear and sublinear conditions, under which the Guo-Krasnosel'skii fixed point theorem is applied in a cone to get the existence of positive solutions. To facilitate this, the corresponding Green's function is constructed, and its essential properties are explored. A number of illustrative examples are included to show the applicability of the theoretical results and emphasize their effectiveness.