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Fractional Differential Equations
- Publisher
- Emerald Publishing
- Copyright
- © Emerald Publishing Limited
- ISSN
- 0332-1649
- DOI
- 10.1108/compel-05-2019-0179
- Publisher site
- See Article on Publisher Site
Abstract
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/approachThis 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.FindingsThe 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/valueThis 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.
Journal
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing
Published: May 20, 2020
Keywords: Electromagnetic fields; Electromagnetic compatability; Soil electrical parameters; Frequency-dependent effect; Maxwell's equation; The puiseux series