The 12th International Conference on Fuzzy Systems and Data Mining (FSDM 2026)

Abstract:
Volterra integral equations (VIEs) are important mathematical tools for modeling systems with memory and have applications in various fields of science, engineering, and applied mathematics. This talk begins with classical (crisp) VIEs and their numerical approximation, before extending the discussion to fuzzy Volterra integral equations, which allow uncertainty in the mathematical description of real-world systems. We then consider a more general class of fuzzy VIEs involving proportional delay and piecewise discontinuous kernels. In this setting, the discontinuity curves are defined by the proportional delay parameter. This structure partitions the original integral equation into several subintervals, each associated with its own continuous kernel and nonlinear term. We also establish the existence and uniqueness of solutions using a Picard-type iteration and the Gronwall inequality. For the numerical solution, we develop a collocation method based on piecewise fuzzy polynomial approximation and apply the Gauss--Legendre quadrature rule separately on each subinterval. We also derive an error bound in terms of the fuzzy modulus of continuity and investigate the performance of the proposed method through numerical examples. The results illustrate the accuracy and effectiveness of the approach for solving fuzzy Volterra integral equations with proportional delay and piecewise discontinuous kernels. The talk thus provides a systematic progression from classical Volterra integral equations to fuzzy formulations and, finally, to delay problems with discontinuous kernels, emphasizing the theoretical and computational challenges at each stage.

Biography: Prof. Samad Noeiaghdam, PhD of Applied Mathematics, is Research Professor of Henan Academy of Sciences, Zhengzhou, China. He was an Associate Professor of Irkutsk National Research Technical University, and a Senior Researcher in South Ural State University, Russia during 2019-2024. His main research interests are numerical analysis, solving mathematical models, fuzzy problems with applications, energy system problems, load leveling in energy storage, supply and demand systems, MHD and heat and mass transfer problems. He has more than 190 publications including several high-quality papers in top journals as well as books, chapters and conference papers. Because of his high-level activities in research and contribution to mathematical advancement globally he has been acknowledged as one of the top 2% scientists by Stanford University. He is the member of editorial board and guest editor in various journals and special issues.