UNIVERSITE ABDERAHMANE MIRA - BEJAIA
Faculté des Sciences Exactes - Laboratoire de Mathématiques Appliquées
Conférence Internationale
« Statistiques et Analyse Avancées : Domaines d'Interactions et d'Applications »
« SAADIA 2 »
Université A. Mira de Bejaia, 17 - 19 Novembre 2025
LES CONFÉRENCIERS THE SPEAKERS
Claudianor Oliveira Alves
Bolsista de Produtividade em Pesquisa do
CNPq - Nível 1C - CA MA - Matemática eEstatística
Title: Existence of normalized solution for some classes of elliptic problems
Abstract: In this talk we will show some recentes result involving the existence of normalized solution for a large class of elliptic problem in bounded in unbounded domain. The main tool used is the variational method, and the main idea is to minimize the energy functional on a special manifold. The audience will see that there are different difficulties when we considering the problem in a bounded our in an unbounded domain.
Hédi Nabli
Laboratory of Probability and Statistics
Faculty of Sciences – University of Sfax
PO 1171, Sfax 3000, Tunisia
Title: Combinatorial analysis, Algebra, trigonometry and their applications among Arab mathematicians
Abstract: The contribution of Arab scholars to mathematics is undeniable, with a vast number of terminologies translated or transcribed from Arabic serving as evidence. Unfortunately, this contribution is often only acknowledged in the history of mathematics books, rather than in textbooks used in schools or universities. In this conference, we will present several rules, theorems, and algorithms derived by Arab scholars, emphasizing that many of these scientific results are either not attributed to their original authors or are mistakenly credited to others. For example, the Al-Karaji triangle is often wrongly attributed to Pascal. We will also review several mathematical applications, categorized by themes, which span various fields. These applications include, among others, Al-Biruni's method for determining the Earth's circumference
and Al-Kashi's algorithm for computing π to 16 decimal places.
Tommaso lando
RTD-B (Associate Professor), University of Bergamo
Title: Nonparametric inference based on expected order statistics
Abstract: As well known, the $j$-th order statistic of a sample of size $m$ from a random variable $X$ is defined as the $j$-th smallest value in the sample and is denoted by $X_{j:m}$. These quantities play an important role in nonparametric inference. Given a random sample of size $n$ (possibly different from $m$) drawn from $X$, we investigate the estimation of the expected order statistics $E[X_{j:m}]$ and, more importantly, the development of novel statistical methods based on these estimators. We introduce L-estimators for the expected order statistics and establish their almost sure (a.s.) consistency, even in scenarios where the mean of $X$ is not finite. Letting $F$ denote the cumulative distribution function (CDF) of $X$, and $G$ a reference (known) distribution, these estimators serve as the foundation for tests assessing the convexity or concavity of the composition $G^{-1}(F)$, as compared to equality in distribution. This approach includes well-known cases, such as distributions with increasing hazard rate, and extends to other relevant distribution families that have recently received growing interest. The proposed tests are shown to be consistent and unbiased. Additionally, we propose a novel nonparametric estimator of the distribution function $F$, constructed from the estimated expected order statistics.
Ivan Area
Escola de Enxenaria Aeronautica e do Espazo
Departamento de Matematica Aplicada II
Universidade de Vigo, Ourense (Spain)
Title: On g-orthogonal polynomials: a theoretical tool arising from applications
Abstract: In this talk we shall present a new class of special functions, by combining the very classical theory of univariate orthogonal polynomials with the Stieltjes derivatives: the g-orthogonal polynomials. Their origin comes from the need of this specific tool in a real-world application: mathematical modeling of the spread of Vespa Velutina, an invasive species that first arrived in Europe in 2004 coming from Asia.
Alexey Karapetyants
Rostov-on-Don, RUSSIA
Title: Hadamard-Bergman operators in weighted spaces
Abstract: We discuss recent study of the Hadamard–Bergman operators in the unit disc of the complex plane. These operators arose as a natural generalization of the orthogonal projector and represent an integral realization of multiplier operators. We give some important examples illustrating the relevance of such research, including the integrodifferentiation operator of variable order and certain Volterra type operators studied in complex analysis earlier. It is worth noting that it is the Hadamard–Bergman operators that seem to lay claim to the most direct complex analogue of operators with homogeneous kernels in the unit disc. This opens up excellent opportunities for further development of the study of operators of the Hadamard–Bergman type.
Delfim F. M. Torres
University of Aveiro, Portugal
Title: Duality Theory, The Fractional Calculus of Variations and the Inverse Problem
Abstract: Utilizing the duality theory of fractional calculus, originally introduced by Caputo and Torres in 2015, we are able to transform left fractional operators into right fractional operators and vice versa through duality [01]. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractional derivative (left or right) is present. This applies to both the problem formulation and the corresponding necessary optimality conditions. As a practical application, we present a new Lagrangian that relies solely on left-hand side fractional derivatives. The fractional variational principle derived from this Lagrangian leads us to the equation of motion for a dissipative/damped system [02]. Finally, we solve the inverse problem of the Fractional Calculus of Variations: given a fractional-order linear equation, we define an appropriate symmetric bilinear form so that the fractional operator is symmetric with respect to that bilinear form. Using the bilinear form, we then use the results of [02] to define a functional of the fractional calculus of variations, proving that the solutions of the given fractional-order equation are critical points of the fractional variational functional. In the case of fractional integral equations, the provided bilinear form is non-degenerate, and all critical points are solutions of the given equation. In the case of fractional differential equations, a relation with the least-squares method is obtained.
Tatiana Odzijewicz
Collegium of Economic Analysis, SGH Warsaw School of Economics
Al. Niepodległosci 162, 02-554 Warsaw, Poland
Title: Applications of the Sturm-Liouville problem to the anomalous diffusion equation: non-local approach
Abstract: We present results regarding the homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.
Dumitru Baleanu
Department of Computer Science and Mathematics, Lebanese American - University,Beirut,Lebanon
Institute of Space Sciences, Magurele-Bucharest, Romania
Title: On Some New Trends in Fractional Calculus and its Applications
Abstract: Fractional calculus deals with the study of so-called fractional order integral and derivative operators over real or complex domains and their applications. In my talk I will present some new trends in this important field related to the geometrical meaning of some modified operators with Mittag-Leffler kernels.
Juan Carlos Cortés López
Instituto Universitario de Matemática Multidisciplinar,
Universitat Politècnica de València, Spain,
Title: EQUATIONS WITH JUMPS
Bridging Uncertainty And Discontinuities: A Journey Into Random Differential
Abstract: Differential equations serve as powerful mathematical tools for modeling real-world
phenomena. However, their deterministic nature fails to account for both epistemic and aleatoric
uncertainties arising from limited knowledge about the system being modeled and the
unpredictable, inherent randomness of the problem itself. Beyond randomness, many dynamic
processes undergo sudden changes, such as shocks, resource harvesting, or natural disasters. These
abrupt perturbations can be mathematically represented through discontinuities or impulses,
capturing their instantaneous effects.
Addressing both uncertainties and impulses within the framework of differential equations presents
a significant challenge, drawing increasing interest from the scientific community. Notably,
substantial progress has been achieved using stochastic differential equations, where randomness is
typically introduced through processes like white noise and the Poisson process.
This talk will explore recent advancements in uncertainty quantification for differential equations
incorporating jumps and discontinuities, leveraging the random differential equations (RDEs)
framework. In this approach, uncertainties are directly embedded in various components of the
equation —including initial conditions, source terms, and coefficients— using arbitrary probability
distributions. Furthermore, we will introduce a method to determine the probability density function
of the solution, treating it as a stochastic process rather than focusing solely on its first statistical
moments. The theoretical developments will be complemented by simulations and real-world
applications, demonstrating how inverse uncertainty quantification techniques can be used to infer
model parameter distributions from empirical data.
Houda EL Bouhissi
University of Bejaia
Title: Artificial intelligence in healthcare: a revolution of medical practice
Abstract : Artificial Intelligence (AI) has revolutionized healthcare, enabling major advances in diagnosing and treating medical conditions. Today, AI can analyzehealthcare Big Data and help make earlier and more accurate diagnoses.
The use of AI in healthcare is expected to play a major role in redefining the way we process health data, diagnose diseases, develop treatments and even prevent diseases altogether. By using artificial intelligence in healthcare, healthcare professionals will be able to make more informed decisions based on more accurate information. This will save time, reduce costs and improve the management of medical records in general.
In surgery, intelligent robots help doctors carry out safer and less invasive procedures. AI is also making it possible to modify treatments to each patient's genetic profile, covering the way for increasingly personalized medicine. But these advances raise important ethical questions about the privacy of health data, the transparency of algorithms, and fair access to innovation.
This plenary session aims to provide an overview of the practical applications of AI in healthcare, and present the latest innovations, and to open a collective debate on the challenges and responsibilities involved.
Keywords :Artificial intelligence, medical Big Data, Deep Learning,Healthcare, Machine learning, AI-assisted diagnostics, medical robotics, digital health.
Amar Debbouche
University, Guelma, Algeria
Title: Stability and optimal control strategies for epidemiological mathematical model
Abstract: We consider a class of SIR model with quarantine and vaccination compartments. We establish the well-posedness and boundedness results of the considered system. For the main results, a generation matrix and equilibrium points of the model are obtained. In order to manage the transmission of infection within the outlined model, we employ the strategy of optimal control. This approach involves implementing control measures and interventions guided by mathematical optimization techniques to minimize the spread of disease. These control strategies may encompass vaccination campaigns, quarantine protocols, social distancing measures and other preventive actions. Further, to evaluate the effectiveness of proposed model and the applied optimal control strategy, we conduct a series of numerical simulations. Computational results involve running the model under different scenarios, considering a range of parameters and meticulously analyzing the resulting outcomes.
Keywords: Epidemiological model; well-posedness; sensitivity analysis; optimal control; numerical simulation.
