Fractional-Calculus-Based Electromagnetic Tool to Study Pulse Propagation in Arbitrary Dispersive Dielectrics

Fractional calculus is a fruitful field of research in science and engineering. The concept of fractional exponents is an outgrowth of exponents with integer value. In the same way, fractional order of integration is a generalization of the mathematical operations of differentiation and integration to arbitrary, general, noninteger order. Although it better models the higher complexity by nature, it is still fairly easy to physically represent its meaning. However, taking in consideration that the study of fractional calculus theory opens the mind to entirely new branches of thought, in this feature article the authors illustrate as such concept can be an interesting and useful tools in electromagnetic theory to solve specific electromagnetic problems regarding the wave propagation and radiation in arbitrary dispersive dielectric materials. In particular, time fractional Maxwell's equations for media with power-law frequency dispersions are illustrated focusing the attention on the mathematical and computational topics. Moreover, practical examples highlighting their usefulness for understanding a variety of electromagnetic phenomena are provided.