Electric Fractional Order Potencial

In this study we apply the concept of fractional calculus to electromagnetism and we develop a new fractional order approximation method to the electrical potentialThe Maxwell equations play a fundamental role in the well established formulation of the electromagnetic theory [1]. These equations lead to the derivation of precise mathematical models useful in many applications in physics and engineering. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomena present in electrical systems, such as motors, transformers and lines [2,3], and the motivation towards the development of comprehensive models, seem to point out the requirement for a fractional calculus (FC) approach [4]. In an alternative perspective several authors [5] have verified that well-known expressions for the electrical potential are related through integer-order integral and derivatives and have proposed its generalization based on the concept of fractional-order poles. Nevertheless, the mathematical generalization towards FC lacks a comprehensive method for its practical implementation.