Thermodynamics in Fractional Calculus

A generalization of thermodynamics in the formalism of fractional-order derivatives is given. Results of the traditional thermodynamics of Carnot, Clausius, and Helmholtz are obtained in the particular case where the exponent of a fractional-order derivative is equal to unity. A one-parametric "fractal" equation of state is obtained with account of the second virial coefficient. The application of the resulting equation of state in the case of the gas argon is considered.