Work

Solvability for Two-Point Boundary Value Problems for Nonlinear Variable-Order Fractional Differential Systems

Year: 2025

Type: article

Abstract: A class of boundary value problems for fractional differential systems involving variable-order derivatives is considered. Such problems can be transformed into some boundary value problems for nonlinear Caputo fractional differential systems. Here, the relations between linear Caputo fractional differential equations and their corresponding linear integral equations are investigated, and the results demonstrate that a proper Lipschitz-type condition is needed for studying nonlinear Caputo fractional differential equations. Then, an existence and uniqueness result is established in some vector subspaces by Banach’s fixed-point theorem and ∥·∥e norm. In addition, two examples are presented to illustrate the theoretical conclusions.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9090615

Authors: Yige Zhao, Rian Yan

Institutions: University of Jinan, Hunan City University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: National Natural Science Foundation of China, University of Jinan