Controllability Criteria for Type-2 Fuzzy Fractional-order Dynamical System via Mittag-Leffler Matrix Function using granular derivative.
نویسندگان
1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India.
2 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India.
3 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India.
doi
10.22111/ijfs.2024.47862.8422چکیده
This study is concerned with finding the controllability of granular type-2fuzzy fractional-order dynamical control systems (GrT2FuFDCS) usingMittag-Leffler matrix function. Some new concepts concerning to granularinterval valued type-2 fuzzy fractional derivative is introduced inthis paper. To arrive at finding the controllability of the type-2 fuzzydynamical system, type-2 triangular fuzzy function and type-2 triangularfuzzy numbers are used to model fractional dynamical controlsystem. Besides, the controllability Grammian matrix is defined basedon Mittag-Leffler matrix function. Granular fuzzy Laplace transform andinverse Laplace transform are utilized to derive the solution of the type-2 triangular fuzzy fractional-order control systems. The derived resultsensure that the controllability of the proposed GrT2FuFDCS for bothlinear and non-linear case exists. Finally, numerical examples and theirsimulation results are given to illustrate the merit of the obtained results.
