Existence and uniqueness of solutions for a class of fractional differential equation with lower-order derivative dependence

Yujun Cui; Chunyu Liang; Yumei Zou; Yujun Cui; Chunyu Liang; Yumei Zou

doi:10.3934/math.2025176

AIMS Mathematics

2025, Volume 10, Issue 2: 3797-3818. doi: 10.3934/math.2025176

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Existence and uniqueness of solutions for a class of fractional differential equation with lower-order derivative dependence

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 20 December 2024 Revised: 08 February 2025 Accepted: 18 February 2025 Published: 25 February 2025
MSC : 34B10, 34B15

This study investigates boundary value problems for nonlinear fractional-order differential equations. The differential operator is interpreted in the Riemann-Liouville sense and is coupled with a non-linearrrrr term that involves the fractional derivative of the unknown function. Using the Schauder fixed point theorem, the Banach fixed point theorem, and the Leray-Schauder continuation theorem, we establish results regarding the existence and uniqueness of solutions within suitable function spaces. Additionally, we provide concrete examples of various boundary value problems involving fractional-order differential equations to demonstrate the applicability of the theory developed.
Citation: Yujun Cui, Chunyu Liang, Yumei Zou. Existence and uniqueness of solutions for a class of fractional differential equation with lower-order derivative dependence[J]. AIMS Mathematics, 2025, 10(2): 3797-3818. doi: 10.3934/math.2025176

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Abstract

This study investigates boundary value problems for nonlinear fractional-order differential equations. The differential operator is interpreted in the Riemann-Liouville sense and is coupled with a non-linearrrrr term that involves the fractional derivative of the unknown function. Using the Schauder fixed point theorem, the Banach fixed point theorem, and the Leray-Schauder continuation theorem, we establish results regarding the existence and uniqueness of solutions within suitable function spaces. Additionally, we provide concrete examples of various boundary value problems involving fractional-order differential equations to demonstrate the applicability of the theory developed.

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