About the Use of Generalized Forms of Derivatives in the Study of Electromagnetic Problems

Abstract

The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. The case of electric circuits, ruled by non-integer derivatives or capacitors with fractional dielectric permittivity, is a fairly natural frame of relevant applications. We use techniques, involving generalized exponential operators, to obtain suitable solutions for this type of problems and eventually discuss specific problems in applications.

Keywords

• Riemann–Liouville–Caputo 26A42
• fractional derivatives 26A33, 34K37, 34K60
• exponential evolution operators 34L40, 34Lxx, 47Gxx
• electric circuits 47N70
• fractional permittivity 82Dxx