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

Year 2025, Volume: 8 Issue: 3, 158 - 166, 17.09.2025

Hamza Tabti , Fahd Jarad

https://doi.org/10.32323/ujma.1691155

Abstract

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.

Keywords

Caputo , Existence , Fixed point theorem , Fractional differential equation , Green , Sublinear condition , Superlinear condition

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