PLENARY SPEAKERS

Abstract: Adaptive control is often viewed as one approach or paradigm, amongst many, in the feedback control of uncertain systems. These feedback approaches include model reference adaptive controls that “identify” system parameters, and also direct adaptive control approaches that simply “control”. Here we extend this adaptive control paradigm towards learning systems and as mechanisms for emergent complexity. Within this general setting, we specifically consider (i) learning bifurcations and (ii) learning complex behaviours. In mathematical terms, the underpinning asymptotic dynamics are explored through understanding and qualifying the learning systems’ attractor dynamics.

Abstract: In this presentation, I will provide a comprehensive overview of deterministic asset pricing models. I will introduce asset flow differential equations as a framework for modeling a single-asset market consisting of a group of investors and subsequently extend this approach to a two-asset market system. The derivation of these models is based on the assumption of a finite supply of assets, as opposed to unbounded arbitrage opportunities, and incorporates investment strategies driven by either price momentum (trend-following) or valuation-based considerations.

2010 AMS Subject Clasifications: 91B25, 91B50, 91G99

Keywords: Ordinary differential equations for asset pricing, price dynamics, asset flow, dynamical system approach to mathematical finance.

REFERENCES

G. Caginalp, G.B. Ermentrout, Numerical studies of differential equation related to theoritical financial markets, Appl. Math. Lett., 4, 35-38, (1991).
H. Bulut, H. Merdan, D. Swigon, Asset price dynamics for a two-asset market system, Chaos 29, 023114 (2019).
H. Merdan, G. Caginalp, W. C. Troy, Bifurcation analysis a single-group asset flow model, Quarterly Applied Mathematics, Quart. Appl. Math. 74, 275-296, (2016).
H. Merdan, M. Alisen, A mathematical model for asset pricing, Applied Mathematics and Computation, 218, 1449-1456, (2011).
G. Caginalp, H. Merdan, Asset price dynamics with heterogeneous groups, Physica D, 225, 43-54, (2007).
G. Caginalp, Nonlinear price evolution, Quart. Appl. Math., 63, 715-720, (2005).
G. Caginalp, D. Balenovich, Asset flow and momentum: deterministic and stochastic equations, Phil. Trans. R. Soc. Lond. A, 357, 2119-2133, (1999).

Abstract: Predicting the behaviour of physical processes remains a fundamental challenge across scientific disciplines. While traditional computational approaches are often constrained by high costs and practical limitations, artificial intelligence (AI) offers a promising alternative for accurate and effective modelling. This work leverages AI methodologies to develop predictive models that closely mimic real-world process dynamics, even in highly complex scenarios. As a result, rather than emphasizing the importance of physical reality, this study demonstrates how successful artificial intelligence modelling is, even in extremely challenging situations. Our findings not only confirm the robustness of AI in behavioural prediction, but also provide a foundation for novel, scalable approaches to modelling intricate systems. This work contributes to the ongoing paradigm shift in computational science toward data-driven solutions
Keywords: Artificial intelligence modelling, Steep behaviour, Nonlinear behaviour, Realistic process

References

E. Kurul, H. Tunc, M. Sari and N. Guzel “Deep learning aided surrogate modeling of the epidemiological models”, Journal of Computational Science, 84, 102470, 2025.

Loske, A.M. (2017). “Shock waves as used in biomedical applications.” In Medical and Biomedical Applications of Shock Waves (pp. 19-42). Springer.

M. Sari, S. Duran, H. Kutlu, B. Guloglu and Z. Atik, “Various optimized machine learning techniques to predict agricultural commodity prices”, Neural Computing and Applications, 36, 11439-11459, 2024

H. Tunc, M. Sari and E.S. Kotil, “Machine learning aided multiscale modelling of the HIV-1 infection in the presence of NRTI therapy”, PeerJ, 11: e15033, 2023

H.U. Tuna, M. Sari, and T. Cosgun, “A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms”, Physica Scripta, 99(7), 076006, 2024.

M. Sari, I.E. Yalcin, M. Taner, T. Cosgun, and I.I. Ozyigit, “Forecasting contamination in an ecosystem based on a network model”, Environmental Monitoring and Assessment, 195:536, 2023

M. Sari, I.E. Yalcin, M. Taner, T. Cosgun, and I.I. Ozyigit, “An investigation on environmental pollution due to essential heavy metals: a prediction model through multilayer perceptrons”, International Journal of Phytoremediation, 25(1), 89-97, 2023

T. Cosgun and M. Sari, “A novel method to investigate nonlinear advection-diffusion processes”, Journal of Computational and Applied Mathematics, 425, 115057, 2023

H. Tunc and M. Sari, An implicit-explicit local method for parabolic partial differential equations, Engineering Computations, 39(3), pp. 1020-1037, 2022.

M. Sari, T. Cosgun, I.E. Yalcin, M. Taner, and I.I. Ozyigit, “Deciding heavy metal levels in soil based on various ecological information through artificial intelligence modelling”, Applied Artificial Intelligence, 36(1), e2014189, 2022.

S. Gulen, M. Sari and P. Celenk, “Neural network based techniques for steep behaviour represented by nonlinear advection–diffusion-reaction models”, Computational and Applied Mathematics, 44, 300, 2025.

M. Sari, S. Gulen and P. Celenk “Various optimized artificial neural network simulations of advection diffusion processes” Physica Scripta, 99(11), 116016, 2024.

Short biography: Prof. Murat Sarı is an academic in mathematical engineering, specializing in artificial intelligence modelling, numerical methods, and the simulation of nonlinear systems. He completed his Ph.D. at the University of South Wales, UK, with a dissertation on seismic wave modelling using the Boundary Element Method. Currently a professor at Istanbul Technical University, he has served in various high-level academic and administrative roles, including Head of Mathematical Engineering and Rector of ITU-TRNC Education and Research Campuses. Prof. Sarı has authored over a hundred peer-reviewed publications in top-tier journals and has supervised numerous graduate theses in applied mathematics, computational modelling, and biomedical systems. A frequent keynote and plenary speaker, he actively contributes to international academic collaboration, serving on scientific committees, editorial boards, and international project panels. His recent research integrates deep learning with differential equation models, aiming to bridge data-driven and analytical approaches across science and engineering disciplines.

Abstract: The speech will introduce the concept of Generative Artificial Intelligence (GenAI) having with the utilities and risks and emphasizing its role in leveraging mathematical models to innovate and solve problems; discuss recent advancements in GenAI technologies, focusing on improvements in model architectures and notable examples like GPT-3 and AlphaFold; explore the fundamental mathematical concepts behind GenAI, including probability, statistics, and their application in various GenAI architectures; highlight GenAI’s contributions to solving complex mathematical problems and its ability to generate new mathematical data for research; address the technical challenges such as model bias and overfitting, alongside the ethical concerns of GenAI deployment; encourage further interdisciplinary research between mathematicians and GenAI experts; and summarize the potential of GenAI in mathematics and its practical applications, ending with a look at future trends in the field.

Abstract: The fractional calculus is an extension of meaning. So, there are many types of fractional operators. In my presentation, I will discuss some open problems in the area of fractional calculus, particularly about newly introduced modified fractional operators.

Abstract: This talk will explore the challenge of solving algebraic equations over finite fields. This fundamental problem is growing in significance due to its critical applications in coding theory and cryptography. Addressing this problem from theoretical and practical perspectives is essential for advancing these fields. Traditionally, research has focused on determining the number of solutions for specific equations rather than explicitly deriving all possible solutions. While this approach has sufficed for particular applications in cryptographic function theory, a deeper understanding is necessary to achieve more comprehensive results. Expanding the toolkit for solving equations over finite fields will provide valuable resources for theorists, cryptographers, and coding theorists. We will begin by outlining our primary motivations before highlighting significant recent advancements in solving key algebraic equations over finite fields. We will then discuss the underlying methodologies and mathematical concepts that drive these developments and their impact on symmetric cryptography and coding theory.

Abstract: Mathematical modeling is acknowledged to contribute to the comprehension of the way neurological and virological diseases progress while being able to tackle their dynamic and complex mechanisms including subtle attributes and patterns. Utmost attention is to be paid not to compromise accuracy, specificity and reliability to achieve informed decisions, precise and personalized health interventions and accurate diagnosis based on precise classifications by the incorporation of fractal-fractional methods, wavelets, Hidden Markov modeling, and quantum machine learning methods among other applicable ones. Amid these challenges and affordances, quantum Artificial Intelligence (AI) provides the merging of the quantum computing strength with AI, and thus, quantum computing is likely to supercharge the capabilities of AI as a result of removing limitations due to complexity, data size and the time period it takes to solve problems.  Quantum computation as a computational paradigm with quantum computers is capable of solving selected problems via the exploitation of quantum effects such as entanglement and interference. Belonging to the computational complexity theory, quantum complexity theory helps one address complexity classes defined within the use of quantum computers as a computational model governed by quantum mechanics. Quantum   computers are operated on short pulses of light, ensuring practicality owing to the speeding up the computer operations in which the data are converted into quantum bits rather than being directly stored. This kind of storage can be applied to different domains including medicine, neurology, biology, virology, neurovirology, virus biology, healthcare, public health, and so on. All of these benefits point toward quantum supremacy to solve a problem that would not be possible to be solved by classical computers within a reasonable period of time. In the case of the human brain, a heterogeneous medium made up of tissues with cells having various patterns, shapes and sizes distributed across an extra-cellular space along with the numerous synapses forming complex neural networks, an in-depth and accuracy-oriented probing along with the computing of patterns and signatures in individual cells as well as neurons are required. While the human brain is known to excel in pattern recognition, adaptability and parallel processing, quantum computers and computing provide substantial computational power for conducting specific tasks.  Accordingly, the way fractal and multifractional-based predictive optimization model has ensured the classification of subtypes of stroke. Another outcome is the computational complexity modeling of the micro–macrostructural brain tissues with diffusion Magnetic Resonance Imaging MRI signal processing and neuronal multi-components, which has been achieved by means of fractional calculus operators, Bloch–Torrey partial differential equation and Artificial Neural Networks (ANNs). Besides these models, Hidden Markov model and multifractal method within the framework of predictive quantization complexity models has been able to provide for the differential prognosis and differentiation of the subgroups concerning multiple sclerosis (MS). In addition and related to these modes of modeling, methods and techniques, theory of complexity and complex systems with their origins is to be briefly discussed.  Taken together, quantum computing and AI within the foundational characteristics of mathematical modeling with advanced applications provide a framework for the solution of real-life problems towards achieving efficiency and saving time. Furthermore, fractal-fractional and wavelet methods, to cite a few, can be employed for characterizing complex and dynamic patterns in various domains so that specificity, regularity, self-similarity and significant attributes can be detected, which could offer facilitating functions for physicians and clinicians while follow-up procedures, treatment regimens and precision medicine can be efficiently managed so that the life quality of the patients can be maintained.

Keywords: Mathematical neurology; Medical virology; Neurovirology; Virus biology; Quantum computing; Quantum AI; Computational complexity; Quantum complexity theory; ANN; Diffusion MRI signal processing; Wavelet transform modulus maxima; Fractals; Fractional calculus operators; Bloch–Torrey PDE; Hidden Markov.

References:

[1] Karaca, Y. (2025), Mathematical Modeling of Human Hepatitis Medical Virology-based Multifractal Wavelet Analysis by Quantum SVM Computing, Paul Shapshak et al. (Eds): Global Virology V: 21st Century Vaccines and Viruses, Springer.

[2] Karaca, Y. (2023). Fractional calculus operators–Bloch–Torrey partial differential equation–artificial neural networks–computational complexity modeling of the micro–macrostructural brain tissues with diffusion MRI signal processing and neuronal multi-components. Fractals, 31(10), 2340204.

[3] Karaca, Y., Baleanu, D., & Karabudak, R. (2022). Hidden Markov model and multifractal method-based predictive quantization complexity models vis-á-vis the differential prognosis and differentiation of multiple sclerosis’ subgroups. Knowledge-Based Systems, 246, 108694.

[4] Karaca, Y. (2022). Theory of complexity, origin and complex systems. In Multi-Chaos, Fractal and Multi-fractional Artificial Intelligence of Different Complex Systems (pp. 9-20). Academic Press.

[5] Karaca, Y., Moonis, M., & Baleanu, D. (2020). Fractal and multifractional-based predictive optimization model for stroke subtypes’ classification. Chaos, Solitons & Fractals, 136, 109820.

Abstract: The talk addresses basic principles in fractional modeling related to problems merging in nonlocal continua such as heat, mass, and momentum transfer, applied rheology, and other dynamic hereditary models. Two approaches have been considered: the constitutive approach based on fading memory and thermodynamic consistency and formalistic fractionalization. The analysis stresses the attention on the correct model build-up when kernels of various types, dictated by the relaxation behavior of the physical process modeled, have to be applied and their physical and mathematical adequacies.

Abstract: Decision Optimization is a powerful tool that enhances decision-making in complex processes, particularly where the number of possible solutions to a problem is vast and finding the optimal solution is non-trivial. This presentation provides a comprehensive overview of Decision Optimization, beginning with its theoretical foundations and the increasing interest it has generated in both industrial and research settings. The discussion then explores key problem definitions and summarizes leading solution methodologies.

Building on this foundation, the presentation delves into the practical applications of the field across diverse sectors such as logistics, manufacturing, and healthcare. Critical success factors and deployment challenges are highlighted, offering insights into what truly matters in operational environments. As discussed, Decision Optimization can provide significant financial benefits for many companies while accelerating decision-making processes. However, these savings can only be achieved if the solutions are successfully integrated with existing systems, people, and processes. Therefore, special emphasis is placed on the applicability of solution approaches. The session concludes with challenges encountered during deployment, lessons learned, and an outlook on future expectations, aiming to bridge the gap between theory and practice. It is intended for both academic researchers and practitioners seeking to increase awareness and ensure the long-term successful deployment of optimization.

Keywords: Mathematical programming, decision optimization, operations research

Abstract: In this work, we use the operational matrices (OMs) based on Hosoya polynomials (HPs) and collocation method (CM) to obtain numerical solutions for a class of variable order differential equations (VO-DEs). The fractional derivatives and the VO-derivatives are in the Caputo sense. The operational matrices are computed based on the Hosoya polynomials (HPs) of simple paths. Firstly, we assume the unknown function as a finite series by using the Hosoya polynomials as the basis functions. To obtain unknown coefficients of this approximation, we computed the operational matrices of all terms of the main equations.  Then, by using the operational matrix and collocation points, the governing equations are converted to a set of algebraic equations. Finally, an approximate solution is obtained by solving the algebraic equations.

Keywords: Variable order differential equations, Hosoya polynomials, collocation method, operational matrix.

Abstract: Scientific and engineering research has used mathematical modeling to describe, analyze, and predict dynamic systems. We now understand that the integer-order paradigm fails to capture memory effects, long-range dependencies, and hereditary influences in many natural and engineered systems. Fractional calculus is a fascinating and versatile mathematical paradigm that applies differential and integral operators to fractional orders [1]. The method allows dynamical models to directly incorporate memory and nonlocality into their mathematical structure, offering richer and more accurate representations of complex events [2]. Fractional-order models account for past states’ effects on present dynamics, making them useful for modeling viscoelasticity, non-Markovian behavior, fractal geometries, and heterogeneous media. This detailed and critical explanation examines fractional calculus’s role in real-world mathematical modeling [3]. In this talk, beginning with advanced fractional derivatives and integrals’ theory, we discuss their formulations and suitability for different problem classes. Using this foundation, we explore the incorporation of new fractional dynamics into classical differential equations to enhance system behavior models. Next, we use innovative fractional-order techniques to simulate some real-world cases to show their accuracy, versatility, and descriptive power. These case studies demonstrate how advanced fractional models reveal system memory structure and hidden aspects of realistic phenomena. Consequently, this presentation proposes evolving fractional calculus from a specialized mathematical tool to a fundamental modeling paradigm with theoretical depth and practical applicability. The modern fractional approach improves scientists’ and engineers’ analytical tools and prepares them for a new modeling age that can handle real-world systems’ complexity and memory dependence.

Keywords: Modern fractional calculus, mathematical modeling, real-world applications

Abstract: A partial Caputo fractional model blends classical and Riemann-Liouville terms in epidemiology and sociology. The Riemann-Liouville component introduces non-Markovian behavior, lowering transition hazard risk over time. This model generalizes standard Caputo models by combining fractional and classical terms. We prove well-posedness through fixed-point theory, with results on existence, uniqueness, and continuity. Fractional power-series solutions follow a Cauchy-Kovalevskaya-type theorem, and uniqueness relies on Gronwall- and Nagumo-like methods. Linear equations show global existence, series solutions, and stability via Mikusiński calculus. We discuss applications, stochastic extensions, and open conjectures.

Abstract: A numerical method for efficient calculation of recently defined extension of k-beta function, based on quadrature formulas of Gaussian type, is proposed. The modified moments of an even exponential weight function on (−1, 1), with essential singularities at ±1, are calculated in symbolic form in terms of the Meijer G-function. The Mathematica package OrthogonalPolynomials [1] is applied. Also, a new extension of k-gamma and k-beta functions by using two parameter k-Mittag-Leffler function is presented. Many identities of these extensions like symmetric relation, functional relation, generating relations, summation formulas, derivative formulas, integral representations, Mellin transform and generalizing these identities which satisfied by the k-gamma function and k-beta function are studied.

Keywords: k-gamma function, k-beta function, modified moments, Gaussian quadrature rule, orthogonal polynomial, Mellin transform

Abstract: In this talk, we extend the Zakharov-Rubenchik system to the fractional case by using Riesz operators of fractional order in space. We prove that the system is capable of preserving extensions of the mass, energy, momentum and two linear functionals. In a second stage, we propose a discretization to approximate the solutions of our model. In the way, we propose discrete forms of the conserved functionals, and we prove that they are also conserved in the discrete domain. We prove that the numerical scheme has second-order accuracy in both space and time. Moreover, we establish theoretically the properties of conditional stability and second-order convergence of the scheme. The numerical model was implemented computationally, and some simulations are provided in order to illustrate that the method is capable of conserving the discrete functionals and its rate of convergence. This is the first report in the literature in which a multi-conservative fractional extension of this system is proposed, and a numerical scheme to approximate its solutions is designed and fully analyzed for conservative and numerical properties. Even in the integer-order case, this is the first work which proves the approximate conservation of the momentum, and which rigorously proves the stability and the convergence of a scheme for the Zakharov-Rubenchik system.

Short biography: Prof. Dr. Jorge Eduardo Macias-Diaz obtained a PhD in Mathematics from Tulane University of Louisiana under the direction of Prof. László Fuchs (2001) and a PhD in Physics from the University of New Orleans under the supervision of Prof. Ashok Puri (2007). His academic production includes more than 200 journal articles on abstract algebra, nonlinear partial differential equations, mathematical and stochastic modeling, numerical analysis of differential equations, computer simulation of systems in physics, and fractional-order calculus. He has been in charge of various projects financed by the National Council for Science and Technology of Mexico (CONACYT). He is Associate Editor for Applied Numerical Mathematics (Elsevier), International Journal of Computer Mathematics (Taylor and Francis), Advances in Mathematical Physics (Hindawi), and Computational and Mathematical Methods (Wiley). Since 2012, he has been a regular member of the Mexican Academy of Sciences.