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For the Riesz fractional derivative besides the well known integral representation two new differential representations are presented, which emphasize the local aspects of a fractional derivative. The consequences for a valid solution of the fractional Schroedinger equation are discussed.
We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test function.
Accepting the Komar mass definition of a source with energy-momentum tensor $T_{mu u}$, and using the thermodynamic pressure definition, we find a relaxed energy-momentum conservation law. Thereinafter, we study some cosmological consequences of the
Introducing a set ${alpha_i} in R$ of fractional exponential powers of focal distances an extension of symmetric Cassini-coordinates on the plane to the asymmetric case is proposed which leads to a new set of fractional generalized Cassini-coordinate
Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section $sigma_{tot}$ and the $rho$ parameter. The standard picture indicates for $sigma_{tot}$ a leading log-square
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in Fox $H$-func