Mathematical and Computer Modelling of Dynamical Systems

Special Functions and q-Calculus in Mathematical Modelling and Approximation

This Article Collection focuses on special polynomials, degenerate special functions and q-calculus and their applications in mathematical modelling and approximation. We welcome original research that uses these tools to formulate models, study their behaviour, or develop analytical and computational methods for their solution.

Contributions may address the construction of approximation operators, the derivation of exact or approximate solutions, or the analysis of continuous and discrete dynamical systems. Theoretical studies are also welcome when they show how their results can be used in a modelling or approximation problem.

Special polynomials and q-calculus offer useful methods for formulating dynamical models, analysing their behaviour, and approximating their solutions. Their value in applications depends on understanding when these methods work, how accurate they are, and what they reveal about the model. This Special Issue will bring together theoretical and computational studies that address these questions. By connecting results on convergence, stability, and error with concrete modelling problems, it will help researchers choose suitable methods and assess the reliability of their results.

This Collection focuses on the use of special polynomials and q-calculus in the formulation, analysis, and approximation of dynamical models. It welcomes studies that use these methods to describe how a system evolves, derive exact or approximate solutions, or improve the accuracy and efficiency of numerical simulations.

Topics include generating functions and recurrence relations applied to model equations, q-difference equations for discrete dynamical systems, and polynomial or q-based approximation operators for differential, difference, and integral equations arising in modelling. Studies on convergence, stability, and error estimates are welcome when they explain how these results affect the reliability of a model or its numerical solution. Contributions may develop new modelling methods, compare existing methods on a common problem, or validate a model against experimental or observational data. Each contribution should state the modelling problem clearly and explain what the results show about the system or the method used to study it.

The Collection will consider Research Articles.

About the Guest Editors

Dr. Serkan Araci
Serkan Araci is an Associate Professor in the Department of Basic Sciences at Hasan Kalyoncu University, Türkiye. His research focuses on special functions and polynomials, q-calculus, and geometric function theory, with applications to mathematical modelling and approximation. He serves as Editor-in-Chief of Section B (Mathematical and Theoretical Aspects of Modelling) of Mathematical and Computer Modelling of Dynamical Systems. He also holds Editor-in-Chief and Associate Editor positions at other academic journals.

Dr. Taekyun Kim
Taekyun Kim is a Professor of Mathematics at Kwangwoon University in Seoul, Republic of Korea. He received his PhD from Kyushu University in 1994. His research focuses on special functions and polynomials, q-analysis, and p-adic analysis, including the study of q-analogues and degenerate forms of classical polynomial families. He is a founding editor and Editor-in-Chief of Advanced Studies in Contemporary Mathematics and Proceedings of the Jangjeon Mathematical Society. His editorial experience also includes service with Mathematical and Computer Modelling of Dynamical Systems.