Browsing by Author "Pham, Diana"

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    Fractal Signal Processing
    (Springer Birkhauser, 2025) Golmankhaneh, Alireza Khalili; Pham, Diana; Banchuin, Rawid; Sevli, Hamdullah
    This paper presents a novel low-pass filtering framework based on Fractal First \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-order and Second \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-order designs, formulated within the framework of fractal calculus. By incorporating the structure of fractal time, the proposed filters can effectively process signals with intricate, non-differentiable characteristics. The fractal second \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-order low-pass filter is applied to a simulated noisy ECG signal, demonstrating significant noise suppression while preserving the essential morphological features of the waveform. A comparative study with the classical Bessel low-pass filter further illustrates the advantages of the fractal approach in capturing scale-invariant and self-similar properties of biomedical signals. These results highlight the potential of fractal-order filters for advanced biomedical signal processing.
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    Homotopy Perturbation Method for a System of Fractal Schrödinger-Korteweg Vries Equations
    (Springer Heidelberg, 2025) Golmankhaneh, Alireza Khalili; Pham, Diana; Stamova, Ivanka; Ramazanova, Aysel; Rodriguez-Lopez, Rosana
    This paper presents a novel application of the Homotopy Perturbation Method (HPM) to a system of coupled fractal Schr & ouml;dinger-Korteweg-de Vries (S-KdV) equations, formulated within the framework of fractal calculus. By extending classical S-KdV equations and diffusion-reaction systems to fractal space, we introduce a new mathematical model that captures the complex behavior of nonlinear wave interactions and reaction-diffusion processes in media with fractal geometries. The main contribution of this work lies in deriving approximate analytical solutions for these fractal systems using HPM, demonstrating both its effectiveness and accuracy in handling fractal differential equations. The influence of fractal time and space on the system dynamics is examined and visualized through detailed graphical analysis. This study provides a foundation for further exploration of fractal models in physical and engineering contexts, offering insights into how fractality alters classical system behavior.