The Solution Of The Fractional Liouville Equation Using TheRiemannLiouvilleandCaputoFractionalDerivative

Abstract

The aim of this is to study the generalization of classical mechanics rates by relying on statistical mechanics to generalize the Hamiltonian represented in the Liouville equation. In this work, we present a solution to the fractional Liouville equationbyapplyingittothefreegassystemandvibrationusingtheCaputoand Riemann-Liouville definitions with a derivative of order α(where n ≤α ≤n−1).