Fractional calculus-based analysis of soil electrical properties

Abstract

Purpose This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high frequencies exhibits a fractional effect. In addition, for the fractional-order formulation, this paper aims to provide a more accurate numerical algorithm for solving the fractional differential equations. Design/methodology/approach This paper analyzes the frequency-dependence of soil electrical properties based on fractional calculus theory. A collocation method based on the Puiseux series is proposed to solve fractional differential equations. Findings The algorithm proposed in this paper can be used to solve fractional differential equations of arbitrary order, especially for 0.5th-order equations, obtaining accurate numerical solutions. Calculating the impact response of the grounding electrode based on the fractional calculus theory can obtain a more accurate result. Originality/value This paper proposes an algorithm for solving fractional differential equations of arbitrary order, especially for 0.5th-order equations. Using fractional calculus theory to analyze the frequency-dependent effect of soil electrical properties, provides a new idea for ground-related transient calculation.