A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

Mbaye, Mamadou Moustapha; Diop, Amadou; N’Guérékata, Gaston Mandata

doi:10.3390/math13091495

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A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

by

Mamadou Moustapha Mbaye

¹

,

Amadou Diop

^2,3

and

Gaston Mandata N’Guérékata

^4,*

¹

Laboratoire de Mathématiques Appliquées (LMA), Département de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Dakar-Fann BP 5005, Senegal

²

Classes Préparatoires aux Grandes Écoles (CPGE), Thiès BP A10, Senegal

³

Laboratoire d’Analyse Numérique et Informatique, Université Gaston Berger, Saint-Louis BP 234, Senegal

⁴

NEERLab, Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA

^*

Author to whom correspondence should be addressed.

Mathematics 2025, 13(9), 1495; https://doi.org/10.3390/math13091495

Submission received: 27 March 2025 / Revised: 19 April 2025 / Accepted: 25 April 2025 / Published: 30 April 2025

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)

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Abstract

This work is mainly focused on square-mean S-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean S-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze some qualitative properties of this type of processes. These properties, combined with the inequality technique, evolution operator theory, fixed-point theory, and stochastic analysis approach, allow us to establish conditions for the existence and uniqueness of square-mean S-asymptotically Bloch type periodicity of bounded mild solutions for a class of stochastic evolution equations with infinite delay and piecewise constant argument. In the end, examples are given to illustrate the feasibility of our results.

Keywords: stochastic processes; stochastic evolution equations; pseudo-S-asymptotically Bloch type periodic functions

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MDPI and ACS Style

Mbaye, M.M.; Diop, A.; N’Guérékata, G.M. A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument. Mathematics 2025, 13, 1495. https://doi.org/10.3390/math13091495

AMA Style

Mbaye MM, Diop A, N’Guérékata GM. A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument. Mathematics. 2025; 13(9):1495. https://doi.org/10.3390/math13091495

Chicago/Turabian Style

Mbaye, Mamadou Moustapha, Amadou Diop, and Gaston Mandata N’Guérékata. 2025. "A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument" Mathematics 13, no. 9: 1495. https://doi.org/10.3390/math13091495

APA Style

Mbaye, M. M., Diop, A., & N’Guérékata, G. M. (2025). A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument. Mathematics, 13(9), 1495. https://doi.org/10.3390/math13091495

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A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

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