Research Article
Existence and Uniqueness of Mild Solutions for Neutral Stochastic Fractional Sum-Difference Equations with Impulses Driven by a Rosenblatt Process
Yogesh Hanmant Shirole*,
Suryakant Muralidhar Jogdand
Issue:
Volume 14, Issue 5, October 2026
Pages:
277-286
Received:
7 June 2026
Accepted:
14 July 2026
Published:
9 September 2026
Abstract: This paper investigates the existence and uniqueness of mild solutions for a class of neutral stochastic fractional difference equations with impulsive effects in a Hilbert space framework, driven by a Rosenblatt process. The considered system is formulated using the Caputo fractional difference operator and incorporates delay terms, impulsive effects, and stochastic perturbations exhibiting long-range dependence. The primary objective is to establish sufficient conditions ensuring the existence and uniqueness of mild solutions for the proposed system. To achieve this objective, the theory of resolvent operators is combined with stochastic analysis techniques and the Banach fixed point theorem. In particular, an appropriate operator is constructed from the mild solution formulation, and suitable conditions are imposed to guarantee its contractive property. Consequently, the existence and uniqueness of a mild solution are established. The obtained results extend and generalize several existing results for fractional differential and stochastic systems to the discrete fractional setting involving Rosenblatt stochastic processes. The proposed framework effectively accounts for the combined influence of fractional memory, delays, impulsive effects, and long-range-dependent stochastic disturbances. Furthermore, an application to a class of impulsive stochastic partial fractional difference equations is presented to demonstrate the applicability and effectiveness of the theoretical results. The application verifies that the established assumptions can be satisfied in a relevant stochastic fractional model. Thus, the results contribute to the qualitative theory of neutral stochastic fractional difference equations and provide a useful framework for the analysis of discrete-time stochastic systems with memory, delay, impulsive phenomena, and long-range dependence. These findings may also serve as a basis for further investigations of more general stochastic fractional difference systems.
Abstract: This paper investigates the existence and uniqueness of mild solutions for a class of neutral stochastic fractional difference equations with impulsive effects in a Hilbert space framework, driven by a Rosenblatt process. The considered system is formulated using the Caputo fractional difference operator and incorporates delay terms, impulsive effe...
Show More
Research Article
Controlling the Transmission Dynamics of Monkey Pox Infection: A Mathematical Model Approach
Issue:
Volume 14, Issue 5, October 2026
Pages:
287-294
Received:
3 August 2026
Accepted:
17 August 2026
Published:
18 September 2026
DOI:
10.11648/j.ajam.20261405.12
Downloads:
Views:
Abstract: The spread of Monkey Pox (Mpox) poses significant public health challenges, requiring effective intervention strategies to mitigate its impact. This study propose a mathematical model to explore the transmission dynamics of Mpox and assess the impact of quarantine as a control measure. The model divides the population into compartments representing Susceptible, Exposed, Infectious, Quarantined, and Recovered individuals. The system of ordinary differential equations describing the dynamics of the infection were derived. The equilibrium states of the model equations: Disease free equilibrium and Disease endemic equilibrium states were obtained. The stability analysis of the disease free equilibrium was analyzed and found it to be stable. The reproduction number (R0) was obtained and its numerical value was computed. Numerical simulations were performed to investigate how varying quarantine rates affect the progression of the disease across these compartments. The simulations explore the implications of different quarantine intensities on the number of infectious and exposed individuals over time. The results obtained indicate that quarantine can effectively reduce the transmission rate of the infection. Also, it revealed the potential of quarantine to reduce the disease spread and alleviate its overall impact on the population. The findings offered a framework for understanding the dynamics of Mpox transmission and assist public health authorities in designing effective intervention strategies.
Abstract: The spread of Monkey Pox (Mpox) poses significant public health challenges, requiring effective intervention strategies to mitigate its impact. This study propose a mathematical model to explore the transmission dynamics of Mpox and assess the impact of quarantine as a control measure. The model divides the population into compartments representing...
Show More
Research Article
On the Structural Properties of Translations of Neutrosophic Fuzzy Ideals in B-Algebras
Issue:
Volume 14, Issue 5, October 2026
Pages:
295-302
Received:
18 July 2026
Accepted:
30 July 2026
Published:
20 September 2026
DOI:
10.11648/j.ajam.20261405.13
Downloads:
Views:
Abstract: In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characterize neutrosophic fuzzy ideals through their level sets and show that a neutrosophic fuzzy set is a neutrosophic fuzzy ideal if and only if its corresponding level sets are also ideals. We also provide sufficient conditions under which the neutrosophic translation of a neutrosophic fuzzy ideal forms a neutrosophic fuzzy subalgebra. In addition, we introduce the concept of an extension of a neutrosophic fuzzy ideal and prove that the neutrosophic translation of a neutrosophic fuzzy ideal is a neutrosophic fuzzy ideal extension. An illustrative example is presented to demonstrate that not every neutrosophic fuzzy ideal extension is obtained as a translation of a neutrosophic fuzzy ideal. Moreover, we define the multiplication of neutrosophic fuzzy ideals and investigate its properties in B-algebras. We prove that the multiplication of neutrosophic fuzzy ideals is also a neutrosophic fuzzy ideal under appropriate conditions. The results establish meaningful relationships among neutrosophic fuzzy ideals, translations, level sets, extensions, and multiplication in B-algebras. These findings contribute to the development of neutrosophic fuzzy algebraic structures and provide a systematic framework for further investigations of ideals and their associated operations in B-algebras. The proposed characterizations also clarify structural behavior and broaden the existing theoretical framework for neutrosophic fuzzy algebraic systems.
Abstract: In this article, we introduce and investigate the concepts of neutrosophic fuzzy ideals and their translations in B-algebras. We establish the fundamental properties of translations of neutrosophic fuzzy ideals and prove that the translation of a neutrosophic fuzzy ideal of a B-algebra is also a neutrosophic fuzzy ideal. Furthermore, we characteriz...
Show More
,
Felix Tunde Daodu,
Olawale Johnson Olatubi
