Scipedia: RIMNI SPECIAL ISSUE - Advances in Fractional-Order Control or Artificial Intelligence: Methods and Applications

Stability in the Sense of Hyers-Ulam of Proportional Fractional Stochastic Integral Equations

Jesús Sánchez Pinedo — Fri, 02 May 2025 12:37:12 +0200

This work investigates the existence, uniqueness, and stability in the sense of Hyers-Ulam for a class of proportional fractional Itô-Doob stochastic integral equations (PFIDSIE). To establish these properties, we employ the Banach fixed point theorem (BFPT) in combination with several fundamental mathematical inequalities that provide insight into the structure of PFIDSIEs. The approach is structured to demonstrate not only the theoretical foundation of the existence and uniqueness of solutions but also the stability of these solutions in the Hyers-Ulam sense, which ensures that approximate solutions remain close to the exact solution under small perturbations. The results contribute to the broader field of fractional stochastic differential equations, particularly in situations where fractional dynamics and stochastic processes intersect. Furthermore, the findings are illustrated through three examples, showcasing the applicability and utility of the developed theory in practical settings.OPEN ACCESS Received: 29/01/2025 Accepted: 14/03/2025 Published: 20/04/2025

Optimal Control Strategies for COVID-19 Epidemic Management: A Mathematical Modeling Approach Using the SEIQR Framework

Jesús Sánchez Pinedo — Fri, 02 May 2025 12:34:26 +0200

The COVID-19 pandemic has necessitated the development of robust mathematical models to understand and mitigate its impact. This study presents a compartmental model for the Indian pandemic COVID-19 dynamics, incorporating key compartments such as susceptible, exposed, infected, quarantined, and recovered populations. The positivity and boundedness of solutions are rigorously analyzed to ensure that the model remains biologically meaningful over time. A detailed exploration of the basic reproduction number R

Matrix Algorithms Based on Jacobi and Romanovski-Jacobi Polynomials for Solving the FitzHugh-Nagumo Nonlinear Equation

Jesús Sánchez Pinedo — Fri, 02 May 2025 12:33:23 +0200

The present paper develops and makes efficient, a new, state-of-theart numerical technique for solving the FitzHugh-Nagumo Nonlinear Equation (FH-NNE) with initial and boundary conditions, which represents perhaps the simplest mathematical model for discussing biological systems, including nerve signals and cardiac behavior. Which consists of operational matrices and spectral techniques based on Jacobi and Romanovski-Jacobi polynomials. It is ensured that the nonlinear system is modeled so accurately that it can be effectively solved to ensure the best accuracy combined with computational economy. Comparing the results with the respective numerical results, it is seen that the proposed techniques outdo the standard ones as respects accuracy and efficiency of computation.OPEN ACCESS Received: 11/01/2025 Accepted: 25/02/2025 Published: 07/04/2025