2016/12/01 by Selçuk Ş. Bayın, Selçuk Ş. Bayin · 1 citation
Mathematics · Physics and Astronomy · #Anomalous diffusion #Fourier transform #Fractional Differential Equations Solutions #Fractional calculus #Limit (mathematics) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #Quantum #Representation (politics) #Riesz potential #Space (punctuation) #physics.gen-ph
paper · pdf · doi:10.1063/1.4968819
published as Journal of Mathematical Physics, v.57, 123501 (2016)
openalex publication_date 2016/12/01 · arxiv created 2016/12/07 · arxiv updated 2016/12/12 · openalex created_date 2016/12/16 · openalex updated_date 2026/08/05
We investigate and compare different representations of the Riesz derivative, which plays an important role in anomalous diffusion and space fractional quantum mechanics. In particular, we show that a certain representation of the Riesz derivative that is generally given as also valid for order alpha equals 1, behaves no differently than the other definition given in terms of its Fourier transform. In the light of this, we discuss the alpha goes to 1 limit of the space fractional quantum mechanics and its consistency.