Recently, a systematic way for constructing fractional differential equations was proposed. This was done by introducing an arbitrary parameter \(\sigma \) , measured in temporal or spatial units depending on the type of derivative. In the present work, given the fractional differential equation corresponding to the RC circuit and the experimental data obtained in the laboratory, an analysis of the system behavior is made. We observe, that even in a simple system, there is a small discrepancy between the experimental results and the ordinary mathematical model that represents it. We show, that the given model is best represented by its corresponding fractional differential equation of order \(\gamma = 0.98\) and the value of \(\sigma = 48.7985 s\) .

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Modeling a Real Electrical Circuit with Fractional Calculus

  • J. Juan Rosales,
  • Sergio Israel Velázquez Chávez,
  • F. A. Godínez

摘要

Recently, a systematic way for constructing fractional differential equations was proposed. This was done by introducing an arbitrary parameter \(\sigma \) , measured in temporal or spatial units depending on the type of derivative. In the present work, given the fractional differential equation corresponding to the RC circuit and the experimental data obtained in the laboratory, an analysis of the system behavior is made. We observe, that even in a simple system, there is a small discrepancy between the experimental results and the ordinary mathematical model that represents it. We show, that the given model is best represented by its corresponding fractional differential equation of order \(\gamma = 0.98\) and the value of \(\sigma = 48.7985 s\) .