Next Article in Journal
A Temporal Second-Order Difference Scheme for Variable-Order-Time Fractional-Sub-Diffusion Equations of the Fourth Order
Next Article in Special Issue
Existence and Stability of Solutions for p-Proportional ω-Weighted κ-Hilfer Fractional Differential Inclusions in the Presence of Non-Instantaneous Impulses in Banach Spaces
Previous Article in Journal
Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems
Previous Article in Special Issue
The Impulsive Coupled Langevin ψ-Caputo Fractional Problem with Slit-Strip-Generalized-Type Boundary Conditions
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Fractal Fract
Volume 8
Issue 2
10.3390/fractalfract8020111
fractalfract-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

by
Kaihong Zhao
1,*,
Juqing Liu
2 and
Xiaojun Lv
3
1
Department of Mathematics, School of Electronics & Information Engineering, Taizhou University, Taizhou 318000, China
2
School of Mathematics and Information Technology, Yuxi Normal University, Yuxi 653100, China
3
Applied Technology College, Soochow University, Suzhou 215325, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2024, 8(2), 111; https://doi.org/10.3390/fractalfract8020111
Submission received: 3 January 2024 / Revised: 6 February 2024 / Accepted: 9 February 2024 / Published: 13 February 2024
(This article belongs to the Special Issue Boundary Value Problems for Nonlinear Fractional Differential Equations: Theory, Methods and Application)
Versions Notes

Abstract

The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings.
Keywords: impulsive coupled implicit system; CH–fractional derivative; multipoint BVP; solvability and stability; coincidence degree theory impulsive coupled implicit system; CH–fractional derivative; multipoint BVP; solvability and stability; coincidence degree theory

Share and Cite

MDPI and ACS Style

Zhao, K.; Liu, J.; Lv, X. A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory. Fractal Fract. 2024, 8, 111. https://doi.org/10.3390/fractalfract8020111

AMA Style

Zhao K, Liu J, Lv X. A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory. Fractal and Fractional. 2024; 8(2):111. https://doi.org/10.3390/fractalfract8020111

Chicago/Turabian Style

Zhao, Kaihong, Juqing Liu, and Xiaojun Lv. 2024. "A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory" Fractal and Fractional 8, no. 2: 111. https://doi.org/10.3390/fractalfract8020111

APA Style

Zhao, K., Liu, J., & Lv, X. (2024). A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory. Fractal and Fractional, 8(2), 111. https://doi.org/10.3390/fractalfract8020111

Article Metrics

Back to TopTop