SOLVING FPDES & INERTIAL DISCRETE TRANSFER FUNCTION USING ATANGANA-BLAENAU OPERATOR
DOI:
https://doi.org/10.29121/shodhkosh.v5.i5.2024.6235Keywords:
Natural Transform, Homotopy Permutation Method, Fractional Order Transfer Function, Grünwald-Letnikov Definition, ConvergenceAbstract [English]
In this work, the natural homotopy permutation technique is discussed as follows: In order to make this endeavor scientifically valuable, the Atangana-Baleanu operator in the Reimann sense was applied with fractional differential equations to solve them using this method. Definitions and characteristics related to this study are also given, and the algorithm of the methodology is also examined. These equations' approximate solutions were eventually discovered, and the method worked well for resolving this kind of fractional problem.
Fractional order, discrete transfer function model of an elementary inertial plant is proposed. The model uses Atangana-Baleanu operator. The discrete transfer function's convergence and stability are examined. Simulations extend theoretical results. The suggested discrete, approximated model has a minimal numerical complexity and is correct. When modeling various physical phenomena, such as heat processes, it might be helpful.
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