Application of Fractional Calculus to Establish Equations of State for Solid Metals

Abstract

Fractional differ-integral operators are used to obtain the equation of state for a substance that can be seen as fractal. Two equations of state have been obtained, the first of which depends on two parameters that characterize the fractal dimension of the material and the thermal energy of the particles, respectively. The second equation involves three parameters, and expressions for the Helmholtz free energy and the bulk modulus have also been obtained for this equation. The model presented in this study has been validated using experimental data available in literature, and fractional exponent have been determined for various metals.

Keywords

• equation of state
• fractional calculus
• thermodynamics
• fractal materials