Review of the applications of different fractional models in engineering

• Fractional calculus survey of RL, Caputo, GL, CF, and AB for engineering. • Guidance to choose derivatives from physics and boundary conditions. • Use cases: FOPID control, non-Fourier heat, viscoelastic creep, porous flow. • Numerical solvers compared: GL schemes, MABMM, and homotopy methods. • Gaps flagged: parameter estimation, benchmarks, experimental validation. Fractional calculus has emerged as a powerful framework for modeling complex engineering systems characterized by memory effects, non-local interactions, and anomalous behaviors. This review provides a comprehensive analysis of the diverse applications of fractional models across key engineering domains, including control theory, heat transfer, viscoelasticity, fluid mechanics, and signal processing. The discussion highlights how fractional models enhance modeling precision, improve system stability, and offer deeper insights into processes that cannot be accurately captured by traditional integer-order approaches. By synthesizing findings from a wide range of studies, the paper demonstrates the practical advantages of fractional models in solving real-world engineering challenges, such as optimizing control performance, predicting material behavior, and improving signal interpretation. The review also identifies key research gaps related to computational complexity, parameter estimation, and experimental validation, offering future directions for expanding the practical utility of fractional models. Overall, this study underscores the growing relevance of fractional calculus as an essential tool for advancing engineering analysis and design.