Analyzing Fractional Order Systems of RLβCα Circuits: An HF-Based Efficient Approach

The use of fractional calculus in dynamical system modeling and control has grown in popularity. When modeling real-world electrical circuits and systems, standard integer ordering cannot precisely take place. All systems in reality point to equations with fractional or non-integer orders. The modeling and analysis of fractional-order real-life systems can be somewhat challenging if the typical assumptions that simplify system modeling are not taken into account. To handle fractional order systems, like RCα, RLβ, and combinational RLβCα circuits, a sample-based digitally compatible technique is presented in this paper. The proposed approach has used an orthogonal hybrid function (HF) set that is linearly merged with the SHF and TF sets. This work introduces and examines a few predominant fractional-order electrical systems, goes to great lengths to explain how the problem was addressed, and demonstrates the effectiveness of the recommended solution. To validate and demonstrate the effectiveness of the proposed method, a few numerical examples are provided along with relevant graphs and tables, and the results are compared with the exact answer.