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3-4 Dec 2025 Mila (Algeria)
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Plenary Speakers
Title: New regularity results for the fractional heat equation and applications
Title: Nonlinear diffusion fractional boundary-value problems: Theory and numerical approximation Abstract. In various fields of applied sciences, fractional PDEs (FPDEs) have shown an undeniable potential to tweak the classical PDE model approach and control the results. Well-posedness of fractional boundary-value problems (FBVPs) is crucial to correctly model many phenomena. Among others, fixed-point theory is a thriving field of functional analysis providing a powerful tool with diverse applications in many fields. A lot of numerical methods have been developed for PDEs and FPDEs arising in many areas. Along with the classical numerical techniques, other approaches also exist.
Title: Dynamical Systems Methods in Modern Cosmology Abstract: The theory of dynamical systems offers a powerful framework for analyzing cosmological models, particularly those describing homogeneous and isotropic universes. By recasting the cosmological field equations as systems of ordinary differential equations, one can apply techniques such as fixed point analysis, stability theory, and center manifold methods to study the qualitative behaviour of the Universe, including its late-time accelerated expansion. This work provides a self-contained overview of these methods and their application to modern cosmology, aimed at graduate-level researchers in applied mathematics and theoretical physics.
Title: Fractional-Order Adaptive Observers Design For Secure Communication Based on Chaos Control Using Abstract: In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. In the case of nonlinear models and chaotic systems, the recent introduction of fractional order operators has opened a new horizon for researches on control and synchronization of chaotic systems, with an improved efficiency and a larger domain of application especially in secure communication systems. The specialized literature counted many new developments related to novel chaotic fractional-order systems, control schemes, and their applications.
Adaptive observer-based synchronization in chaotic systems with unknown slowly time-varying parameters, crucial for parameter modulation-based secure communication systems, is impeded by conventional integer-order adaptive observers’ performance limitations. To overcome this, we introduce a novel Luenberger-like observer incorporating fractional-order gradient adaptation laws. Based on the recent advances in fractional-order calculus and the Lyapunov stability theorem, these adaptation laws guarantee observation errors stability and convergence of their quadratic norm mean value. By optimizing the differentiation order, we minimize a system performance cost function, enhancing both state and unknown parameter estimation accuracy. Numerical simulations with the Chua circuit demonstrate an increase in convergence speed and an improvement in parameter estimation accuracy over the prior scheme with integer order adaptation laws. This advancement in master–slave synchronization enables the development of more robust secure communication protocols in forthcoming studies, paving the way for more reliable and efficient secure communication systems. In a second contribution, we present a novel adaptive observer design for nonlinear fractional-order Lipschitz systems with unknown, slowly time-varying parameters. Drawing on recent advancements in fractional-order calculus, a rigorous stability analysis is conducted, deriving the updating law and formulating the observer’s viability and stability conditions in terms of linear matrix inequalities (LMIs) and linear matrix equalities (LMEs). The proposed observer ensures the stability of both state observation and parameter estimation errors, along with the asymptotic convergence of the observation error norm square mean value to zero. Empirical results from a case study on a fractional-order financial system validate the efficacy of the proposed observer, thereby advancing the field of states and parameters estimation theory for non-integer order nonlinear systems.
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