Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery

Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted 2D slide sequences is proposed. We demonstrate, that the step from a local to a nonlocal algorithm yields an order of magnitude in accuracy and by using the specific fractional approach an additional factor 2 in accuracy of the derived results.Comment: 5 pages, 3 figures, draft for proceedings IFAC FDA12 in Nanjing, Chin

On The Space-Time Fractional Schr\"{o}dinger Equation with time independent potentials

This paper is about the fractional Schr\"{o}dinger equation (FSE) expressed in terms of the quantum Riesz-Feller space fractional and the Caputo time fractional derivatives. The main focus is on the case of time independent potential fields as a Dirac-delta potential and a linear potential. For such type of potential fields the separation of variables method allows to split the FSE into space fractional equation and time fractional one. The results obtained in this paper contain as particular cases already known results for FSE in terms of the quantum Riesz space fractional derivative and standard Laplace operator.Comment: 9 pages. The corresponding author thanks Haidar Khajah, Ram Saxena and Hans Haubold for the valuable discussions and comment