On continuity results for some differential equations with Caputo-Fabrizio derivative

Ho Duy Binh; Nguyen Dinh Huy; Luu Vu Cam Hoan; Nguyen Huu Can

doi:10.15672/hujms.1670526

On continuity results for some differential equations with Caputo-Fabrizio derivative

Abstract

In this paper, we study a differential equation with the Caputo-Fabrizio derivative. First, for a given function $f$, we focus on the convergence results of the Caputo-Fabrizio derivative of $f$ and the first derivative of $f$. We also study the continuity results for fractional-order Caputo-Fabrizio derivative. The second result is considering continuity results for the mild solution to linear problems. The third result mentions the continuity results for the mild solution to nonlinear problem. Additionally, numerical examples are investigated to verify some of the theoretical result.

Keywords

References

[1] S. Abbas, M. Benchohra and J.J. Nieto, Caputo-Fabrizio fractional differential equations with instantaneous impulses, AIMS Math 6 (3), 2932-2946, 2021.

Details

Primary Language

English

Subjects

Partial Differential Equations

Journal Section

Research Article

Authors

Ho Duy Binh This is me
0000-0003-1925-4601
Vietnam

Nguyen Dinh Huy This is me
0000-0002-3755-0757
Vietnam

Luu Vu Cam Hoan This is me
0009-0007-2868-4925
Vietnam

Nguyen Huu Can ^*
0000-0001-6198-1015
Vietnam

Early Pub Date

December 30, 2025

Publication Date

December 30, 2025

Submission Date

April 6, 2025

Acceptance Date

October 17, 2025

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.15672/hujms.1670526

IZ

https://izlik.org/JA84ML37ES

Cite

RIS / Bibtex

APA

Binh, H. D., Huy, N. D., Cam Hoan, L. V., & Can, N. H. (2025). On continuity results for some differential equations with Caputo-Fabrizio derivative. Hacettepe Journal of Mathematics and Statistics, Advanced Online Publication. https://doi.org/10.15672/hujms.1670526

AMA

1.Binh HD, Huy ND, Cam Hoan LV, Can NH. On continuity results for some differential equations with Caputo-Fabrizio derivative. Hacettepe Journal of Mathematics and Statistics. 2025;(Advanced Online Publication). doi:10.15672/hujms.1670526

Chicago

Binh, Ho Duy, Nguyen Dinh Huy, Luu Vu Cam Hoan, and Nguyen Huu Can. 2025. “On Continuity Results for Some Differential Equations With Caputo-Fabrizio Derivative”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1670526.

EndNote

Binh HD, Huy ND, Cam Hoan LV, Can NH (December 1, 2025) On continuity results for some differential equations with Caputo-Fabrizio derivative. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication

IEEE

[1]H. D. Binh, N. D. Huy, L. V. Cam Hoan, and N. H. Can, “On continuity results for some differential equations with Caputo-Fabrizio derivative”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi: 10.15672/hujms.1670526.

ISNAD

Binh, Ho Duy - Huy, Nguyen Dinh - Cam Hoan, Luu Vu - Can, Nguyen Huu. “On Continuity Results for Some Differential Equations With Caputo-Fabrizio Derivative”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (December 1, 2025). https://doi.org/10.15672/hujms.1670526.

JAMA

1.Binh HD, Huy ND, Cam Hoan LV, Can NH. On continuity results for some differential equations with Caputo-Fabrizio derivative. Hacettepe Journal of Mathematics and Statistics. 2025. doi:10.15672/hujms.1670526.

MLA

Binh, Ho Duy, et al. “On Continuity Results for Some Differential Equations With Caputo-Fabrizio Derivative”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Dec. 2025, doi:10.15672/hujms.1670526.

Vancouver

1.Ho Duy Binh, Nguyen Dinh Huy, Luu Vu Cam Hoan, Nguyen Huu Can. On continuity results for some differential equations with Caputo-Fabrizio derivative. Hacettepe Journal of Mathematics and Statistics. 2025 Dec. 1;(Advanced Online Publication). doi:10.15672/hujms.1670526