Search

We use the unified transform method (UTM) to solve initial-boundary value problems for the fractional advection-diffusion-type equation (FADE) on the real half line. We generalize this equation using the modified definition of the Atangana-Baleanu fractional derivative of order α ∈ (0, 1] in order to satisfy the initial condition. A solution methodology is proposed when the UTM is implemented in fractional differential equations with boundary conditions of Dirichlet and Robin type, in particular when using the modified definitions of fractional operators with non-singular kernel. In addition, an interface problem is stated and solved in the adjacent domains R+ and R-, where perfect contact continuity conditions are imposed. The exact solutions obtained include as a particular case, the diffusion and advection-diffusion equations with integer-order derivatives. Finally, representative curves for the solution are shown by varying the fractional order. [ABSTRACT FROM AUTHOR]

Environmental trends and ecosystems' ranges of variability are little known in tropical very high elevation Andean ecosystems (above 4400 m a.s.l.). We combined satellite image analyses and dendrochronological methods with instrumental records at lower elevation to assess changes in lake size and indices of plant productivity of subtropical high-elevation ecosystems in northern Argentina and southern BoLivia. Between 1985 and 2009, interannual lake fluctuations assessed with Landsat images were positively correlated with interan-nual variations in regional precipitation and de Martonne's aridity index, showing a decreasing trend in moisture availability during the period. Changes in lake size were positively correlated with radial growth of Polylepis tarapacana, and with MODIS-derived phenological parameters of enhanced vegetation index (EVI; an index of vegetation "greenness") between 2001 and 2010. This indicates that water balance has a significant effect on ecosystem functioning, which is related to regional scale atmospheric circulation. A long-term tree ring chronology (starting in 1750) showed that tree growth during recent decades was lower than the last 180 years, and were comparable to growth patterns that occurred between 1775 and 1825. These results suggest that if recent climatic trends continue, long-term ranges of variability in ecosystem functioning could be exceeded. [ABSTRACT FROM AUTHOR]