About the minimum time transference in a fractional differential equation

The use of fractional calculus when modeling phenomena allows new queries concerning the deepest parts of the physical laws involved in. Here we will be dealing with an apparent paradox in which the time of transference from zero in a system with fractional derivatives can be strictly shortened relatively to the minimal time transference done in an equivalent system in the frame of the entire derivatives.

Effects of a mixed vector-scalar kink-like potential for spinless particles in two-dimensional space time

The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink- like potentials (similar to tanh gamma x) is investigated. The problem is mapped into the exactly solvable Sturm - Liouville problem with the Rosen - Morse potential and exact bounded solutions for particles and antiparticles are found. The behavior of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.