Granular Fuzzy Fractional Continuous-Time Linear Systems: Roesser and Fornasini–Marchesini Models - Ghulam Muhammad; Muhammad Akram; Hamed Alsulami; Nawab Hussain (Fractal and Fractional)
In this article, we introduce and investigate two classes of fuzzy fractional two-dimensional continuous-time (FFTDCT) linear systems to deal with uncertainty and fuzziness in system parameters. First, we analyze FFTDCT linear systems based on the Roesser model, incorporating fuzzy parameters into the state-space equations. The potential solution of the fuzzy fractional system is obtained using a two-dimensional granular Laplace transform approach. Second, we examine FFTDCT linear systems described by the second Fornasini–Marchesini (FM) model, where the state-space equations involve two-dimensional and one-dimensional partial fractional-order granular Caputo derivatives. We determine the fuzzy solution for this model by applying the two-dimensional granular Laplace transform. To enhance the validity of the proposed approaches, real-world applications, including signal processing systems and wireless sensor network data fusion, are solved to support the theoretical framework and demonstrate the impact of uncertainty on the system’s behavior.