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Öğe A numerical study of the fractional SIR epidemic model of an infectious disease via the reproducing kernel Hilbert space method(Elsevier, 2025) Nourhane Attia; Ali AkgülIn this chapter, we explore the application of the reproducing kernel Hilbert-space (RK-HS) method to solve a fractional SIR epidemic model that is non-linear with unidentified parameters. This model is of significant importance in epidemiology and medical science for understanding the dynamics of disease spread and control. Our contribution lies in the application of the RK-HS method to this particular fractional SIR model, which, to the best of our knowledge, has not been previously explored. The RK-HS method demonstrates consistent convergence between exact and numerical solutions, making it a valuable tool for solving fractional differential equations. Its mesh-free nature adds to its simplicity and effectiveness. The numerical results are discussed, demonstrating the method's efficiency and accuracy through a comparison with the Adomian decomposition method. Our study concludes that the RK-HS method is a powerful and effective tool for solving non-linear fractional SIR models and offers valuable insights into the dynamics of infectious-disease propagation. The method's versatility in handling complex mathematical models paves the way for further research and applications in a variety of scientific fields.Öğe NUMERICAL METHOD FOR SOLVING PSEUDO-HYPERBOLIC EQUATIONS WITH PURELY INTEGRAL CONDITIONS IN REPRODUCING KERNEL HILBERT SPACE(Wilmington Scientific Publisher, LLC, 2025) Hadjer Zerouali; Ahcene Merad; Ali Akgül; Douha Saadi; Nourhane Attia; Evren HincalThis paper studies a pseudo-hyperbolic equation with purely integral conditions using the reproducing kernel Hilbert space method (RKHSM). By leveraging the properties of reproducing kernel functions (RKFs), we derive exact and approximate solutions to the equation. We present three numerical examples to assess our approach's efficiency and accuracy. The results demonstrate that the RKHSM yields highly accurate approximations, underscoring its effectiveness as a reliable method for solving pseudo-hyperbolic equations with integral constraints. Our findings contribute to the growing research on analytical and numerical techniques for solving such equations.