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Mathematics
Volume 13
Issue 24
10.3390/math13243999
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Existence of Mild Solutions to Impulsive Fractional Equations with Almost-Sectorial Operators

by
Mostefa Seghier
1,*,
Kadda Maazouz
2,* and
Rosana Rodríguez-López
3,4,*
1
Department of Sciences and Technology, Ibn Khaldoun University of Tiaret, Tiaret 14000, Algeria
2
Department of Mathematics, Ibn Khaldoun University of Tiaret, Tiaret 14000, Algeria
3
CITMAga, 15782 Santiago de Compostela, Spain
4
Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(24), 3999; https://doi.org/10.3390/math13243999
Submission received: 13 October 2025 / Revised: 9 December 2025 / Accepted: 11 December 2025 / Published: 15 December 2025
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
Versions Notes

Abstract

This study investigates the existence of mild solutions to impulsive fractional differential equations involving almost-sectorial operators. Through the application of solution operator techniques, fixed-point theory, and Laplace transform, we demonstrate the existence of a unique mild solution to the considered system.
Keywords: impulsive fractional differential equations; mild solution; sectorial operators; fixed-point theory; Laplace transform impulsive fractional differential equations; mild solution; sectorial operators; fixed-point theory; Laplace transform

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MDPI and ACS Style

Seghier, M.; Maazouz, K.; Rodríguez-López, R. Existence of Mild Solutions to Impulsive Fractional Equations with Almost-Sectorial Operators. Mathematics 2025, 13, 3999. https://doi.org/10.3390/math13243999

AMA Style

Seghier M, Maazouz K, Rodríguez-López R. Existence of Mild Solutions to Impulsive Fractional Equations with Almost-Sectorial Operators. Mathematics. 2025; 13(24):3999. https://doi.org/10.3390/math13243999

Chicago/Turabian Style

Seghier, Mostefa, Kadda Maazouz, and Rosana Rodríguez-López. 2025. "Existence of Mild Solutions to Impulsive Fractional Equations with Almost-Sectorial Operators" Mathematics 13, no. 24: 3999. https://doi.org/10.3390/math13243999

APA Style

Seghier, M., Maazouz, K., & Rodríguez-López, R. (2025). Existence of Mild Solutions to Impulsive Fractional Equations with Almost-Sectorial Operators. Mathematics, 13(24), 3999. https://doi.org/10.3390/math13243999

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