The main objective of this paper is to propose a new generalisation of the Helmholtz decomposition theorem for both fractional time and space, which leads to four equations generalising the Maxwell equations that emerge as particular case. To get these results the well-known classical vectorial operators, gradient, divergence, curl, and laplacian are generalised to fractional orders using Grünwald-Letnikov approach.
|Number of pages||14|
|Journal||Communications In Nonlinear Science And Numerical Simulation|
|Publication status||Published - May 2015|
- Fractional curl
- Fractional divergence
- Fractional gradient
- Fractional laplacian