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Fractal Fract
Volume 9
Issue 9
10.3390/fractalfract9090571
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Existence and Nonexistence of Nontrivial Solutions for Fractional Advection–Dispersion Equation with Instantaneous and Non-Instantaneous Impulses

by
Dandan Min
1,* and
Limin Guo
2
1
College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
2
School of Science, Changzhou Institute of Technology, Changzhou 213002, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(9), 571; https://doi.org/10.3390/fractalfract9090571
Submission received: 12 July 2025 / Revised: 21 August 2025 / Accepted: 26 August 2025 / Published: 30 August 2025
Versions Notes

Abstract

In this paper, we consider a class of fractional advection–dispersion equations involving instantaneous and non-instantaneous impulses. The existence of nontrivial solutions is established via Bonanno and D’Aguì’s critical point theorem. Under suitable conditions, we further prove the nonexistence of nontrivial solutions, which is the new result. Additionally, the application of our main results is demonstrated through two examples.
Keywords: fractional advection–dispersion equations; non-instantaneous impulses; variational method; instantaneous impulses fractional advection–dispersion equations; non-instantaneous impulses; variational method; instantaneous impulses

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MDPI and ACS Style

Min, D.; Guo, L. Existence and Nonexistence of Nontrivial Solutions for Fractional Advection–Dispersion Equation with Instantaneous and Non-Instantaneous Impulses. Fractal Fract. 2025, 9, 571. https://doi.org/10.3390/fractalfract9090571

AMA Style

Min D, Guo L. Existence and Nonexistence of Nontrivial Solutions for Fractional Advection–Dispersion Equation with Instantaneous and Non-Instantaneous Impulses. Fractal and Fractional. 2025; 9(9):571. https://doi.org/10.3390/fractalfract9090571

Chicago/Turabian Style

Min, Dandan, and Limin Guo. 2025. "Existence and Nonexistence of Nontrivial Solutions for Fractional Advection–Dispersion Equation with Instantaneous and Non-Instantaneous Impulses" Fractal and Fractional 9, no. 9: 571. https://doi.org/10.3390/fractalfract9090571

APA Style

Min, D., & Guo, L. (2025). Existence and Nonexistence of Nontrivial Solutions for Fractional Advection–Dispersion Equation with Instantaneous and Non-Instantaneous Impulses. Fractal and Fractional, 9(9), 571. https://doi.org/10.3390/fractalfract9090571

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