A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations

Svetlin G. Georgiev; Sibel Doğru Akgöl

doi:10.31801/cfsuasmas.1779784

A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations

Abstract

We establish novel existence criteria for solutions to a class of third-order impulsive nonlinear dynamic equations on time scales, subject to homogeneous boundary conditions. Although first and second-order impulsive dynamic equations are well studied, the analysis of third-order problems remains comparatively underdeveloped. To address this gap, we employ very recent advancements in fixed point theory, utilizing innovative concepts involving expansive mappings and operator addition. This approach enables us to first prove the existence of at least one solution and subsequently demonstrate the presence of at least two distinct solutions. A significant advantage of our methodology is that it does not impose restrictions on boundedness on the nonlinear components of the equation, a requirement common in most existing studies. The applicability and practical relevance of our theoretical results are validated through an illustrative example.

Keywords

References

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Svetlin G. Georgiev
0000-0001-8015-4226
France

Sibel Doğru Akgöl ^*
0000-0003-3513-1046
Türkiye

Publication Date

September 26, 2026

Submission Date

September 8, 2025

Acceptance Date

March 5, 2026

Published in Issue

Year 2026 Volume: 75 Number: 3

DOI

https://doi.org/10.31801/cfsuasmas.1779784

IZ

https://izlik.org/JA67UX96GH

Cite

RIS / Bibtex

APA

Georgiev, S. G., & Doğru Akgöl, S. (2026). A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 75(3), 472-486. https://doi.org/10.31801/cfsuasmas.1779784

AMA

1.Georgiev SG, Doğru Akgöl S. A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75(3):472-486. doi:10.31801/cfsuasmas.1779784

Chicago

Georgiev, Svetlin G., and Sibel Doğru Akgöl. 2026. “A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 (3): 472-86. https://doi.org/10.31801/cfsuasmas.1779784.

EndNote

Georgiev SG, Doğru Akgöl S (September 1, 2026) A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 3 472–486.

IEEE

[1]S. G. Georgiev and S. Doğru Akgöl, “A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 75, no. 3, pp. 472–486, Sept. 2026, doi: 10.31801/cfsuasmas.1779784.

ISNAD

Georgiev, Svetlin G. - Doğru Akgöl, Sibel. “A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75/3 (September 1, 2026): 472-486. https://doi.org/10.31801/cfsuasmas.1779784.

JAMA

1.Georgiev SG, Doğru Akgöl S. A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75:472–486.

MLA

Georgiev, Svetlin G., and Sibel Doğru Akgöl. “A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 75, no. 3, Sept. 2026, pp. 472-86, doi:10.31801/cfsuasmas.1779784.

Vancouver

1.Svetlin G. Georgiev, Sibel Doğru Akgöl. A Novel Application of Expansive Mappings and Cone Theory for Third-Order Impulsive Dynamic Equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026 Sep. 1;75(3):472-86. doi:10.31801/cfsuasmas.1779784