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...
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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
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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...
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,
Felix Tunde Daodu,
Olawale Johnson Olatubi
