  In order to describe more complex problem using the concept of fractional
derivatives, we introduce in this paper the concept of fractional derivatives
with orders. The new definitions are based upon the concept of power law
together with the generalized Mittag-Leffler function. The first order is
included in the power law function and the second is in the generalized
Mittag-Leffler function. Each order therefore plays an important rule while
modelling for instance problems with two layers with different properties. This
is the case for instance in thermal science for a reaction diffusion within a
media with two different layers with different properties. Another case is that
of groundwater flowing within an aquifer where geological formation is formed
with two layers with different properties. The paper presents new useful
information within the scope of fractional calculus that will open new doors
for research and investigations in modelling real world problems.
