Fractional electromagnetics
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J. A. Tenreiro Machado
Abstract
This chapter addresses the application of fractional calculus (FC) in the area of electromagnetics, and studies four cases, namely the modeling of the electric potential generated by arbitrary charges, electric transmission lines, the skin effect in an electric conductor, and the behavior of a nonlinear electric inductor. The first generalizes the concept of integer to fractional electrostatic multipoles. The second interprets the telegraph equation in the light of FC. The third generalizes the skin effect to inductive effects of any fractional order. The fourth, focuses the modeling of inductors, including phenomena usually overlooked with classical approaches.
Abstract
This chapter addresses the application of fractional calculus (FC) in the area of electromagnetics, and studies four cases, namely the modeling of the electric potential generated by arbitrary charges, electric transmission lines, the skin effect in an electric conductor, and the behavior of a nonlinear electric inductor. The first generalizes the concept of integer to fractional electrostatic multipoles. The second interprets the telegraph equation in the light of FC. The third generalizes the skin effect to inductive effects of any fractional order. The fourth, focuses the modeling of inductors, including phenomena usually overlooked with classical approaches.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
