A Dimensional Consistency Aware Time Domain Analysis of the Generic Fractional Order Biquadratic System

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Research Article: A Dimensional Consistency Aware Time Domain Analysis of the Generic Fractional Order Biquadratic System
Author: Rawid Banchuin and Roungsan Chaisricharoen
Email: rawid.ban@siam.edu
Department/Faculty Graduate Schools of IT, Siam University, Bangkok 10160
Published: Journal of Mobile Multimedia, Vol. 183,789–806.doi: 10.13052/jmm1550-4646.18316

Citation 

Banchuin, R., & Chaisricharoen R. (2022). A dimensional consistency aware time domain analysis of the generic fractional order biquadratic system. Journal of Mobile Multimedia, 18(3), 789–806.doi: 10.13052/jmm1550-4646.18316


ABSTRACT

In this research, the time domain analysis of the fractional order biquadratic system with nonzero input and nonzero damping ratio has been performed. Unlike the previous works, the analysis has been generically done with dimensional consistency awareness without referring to any specific physical system where nonzero input and nonzero damping ratio have been allowed. The fractional differential equation of the system has been derived and analytically solved. The physical measurability of the dimensions of the fractional derivative terms which have been defined in Caputo sense, and response with significantly different dynamic from its dimensional consistency ignored counterpart have been obtained due to our dimensional consistency awareness. The resulting solution is applicable to the fractional biquadratic systems of any kind with any physical nature. Based on such solution and numerical simulations, the influence of the fractional order parameter to all major time domain parameters have been studied in detailed. The obtain results provide insight to the fractional order biquadratic system with dimensional consistency awareness in a generic point of view.

Keywords: fractional order biquadratic system, fractional differential equation, fractional time component parameter, dimensional consistency, time domain analysis.


A Dimensional Consistency Aware Time Domain Analysis of the Generic Fractional Order Biquadratic System

Graduate Schools, Siam University, Bangkok, Thailand

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