Numerical model of gas flow in pipeline using fractional time derivatives

Abstract

The paper presents a method for solving systems of nonlinear differential equations in partial
derivatives. A modified finite element method using the Grünwald-Letnikov algorithm for fractional
time derivatives is constructed. Fractional derivatives of Caputo and Riemann-Liouville are
considered. A numerical analysis using experimental data input is carried out. The results of the
experiment confirm the behavior of the gas pressure in the presence of atypical filtering. It is
established that the order of fractional derivative can serve as an adaptation parameter of the
mathematical model.