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


  • Rawid Banchuin Graduated school of IT and Faculty of Engineering, Siam University, Bangkok, Thailand https://orcid.org/0000-0003-4392-8493
  • Roungsan Chaisricharoen School of IT, Meafahluang University, Chiangrai, Thailand




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


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.


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Author Biographies

Rawid Banchuin, Graduated school of IT and Faculty of Engineering, Siam University, Bangkok, Thailand

Rawid Banchuin received the B.Eng. degree in electrical engineering from Mahidol University, Bangkok, Thailand in 2000, the degree of M.Eng. in computer engineering and Ph.D. in electrical and computer engineering from King Mongkut’s University of Technology Thonburi, Bangkok, Thailand in 2003 and 2008 respectively. At the present, he is an associate professor of the Graduated School of Information Technology and Faculty of Engineering, Siam University, Bangkok, Thailand. His research areas include computation and mathematics in electrical and electronic engineering especially the fractional order and memristive devices, circuits, and systems.

Roungsan Chaisricharoen, School of IT, Meafahluang University, Chiangrai, Thailand

Roungsan Chaisricharoen received B.Eng., M.Eng. and Ph.D. degrees from the department of computer engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand. He is an assistant professor at the school of information technology, Mae Fah Luang University, Chiang Rai, Thailand. His research areas include computational intelligence, analog circuits and devices, wireless networks, and optimization techniques.


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