Recently I've developed some equations that involve the fractional Laplacian operator. Because I am very unfamiliar with the fractional Laplacian therefore I am not sure if they can be solved normally. One of them looks like this
(-ℏA/r)(-∆)^(1/2)ψ+ℏE(-∆)^(1/2)ψ=mDψ
Please refer to my paper entitled A TEMPORAL DYNAMICS: A GENERALISED NEWTONIAN AND WAVE MECHANICS posted on ResearchGate for more details.
Working Paper A TEMPORAL DYNAMICS: A GENERALISED NEWTONIAN AND WAVE MECHANICS
Fractional laplacian are one of the topics in the field of fractional calculus. If you are interested in dispersive properties, then let me inform you that Fourier transform property of derivatives applies on fractional derivatives too. You can find this in any standard book of fractional calculus, in particular by Podlubny or Mainardi. Or, See section 3 or equation 15 in this link. https://www.researchgate.net/publication/287249513_Connecting_the_grain-shearing_mechanism_of_wave_propagation_in_marine_sediments_to_fractional_calculus
Secondly, numerical schemes have been developed to solve equations containing fractional derivatives. Eg. Adomian decomposition and Homotopy methods.
Article Connecting the grain-shearing mechanism of wave propagation ...
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Statistical Software
- R