Work

Numerical and Stability Analysis of Hilfer-Type Fuzzy Fractional Control Systems with Infinite Delay

Year: 2026

Type: article

Abstract: This paper presents a unified theoretical and numerical investigation of Hilfer-type fuzzy fractional control systems with infinite continuous delay. By employing contraction mapping principles and compact semigroup theory, we establish rigorous solvability conditions together with Ulam–Hyers–Rassias stability results expressed in terms of Mittag–Leffler functions. To complement the analytical framework, we design and implement numerical schemes based on Euler and IMEX approaches, which confirm the theoretical predictions through simulations. The computational experiments demonstrate the robustness of the proposed framework under delayed feedback and fractional memory effects, highlighting its relevance to practical domains such as biological regulation, porous media transport, and intelligent traffic systems. The contribution of this study lies in the bridge between mathematical rigor and computational implementation, thus advancing the theory of fractional differential inclusions and providing a versatile tool for the stability analysis and control of complex systems with uncertainty and hereditary dynamics.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10040262

Author: Aeshah Abdullah Muhammad Al-Dosari

Institution: Prince Sattam Bin Abdulaziz University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Prince Sattam bin Abdulaziz University