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Properties of fractional derivative complex modulus. (A and B) The real part (A) and the imaginary part (B) are of the complex modulus are referred to as the elastic (or storage) modulus and the viscous (or loss) modulus, respectively. (Insets) Log-log plots of elastic and viscous moduli against frequency exhibit linear relationships with a slope of k. (C) A plot of viscous versus elastic moduli likewise shows a linear relationship that intercepts the origin and has slope tan(kπ/2).
