EN
Fractional calculus is the branch of mathematical
analysis that deals with operators interpreted
as derivatives and integrals of non-integer order. This
mathematical representation is used in the description of
non-local behaviors and anomalous complex processes.
Fourier’s lawfor the conduction of heat exhibit anomalous
behaviors when the order of the derivative is considered
as 0 < β,ϒ ≤ 1 for the space-time domain respectively.
In this paper we proposed an alternative representation of
the fractional Fourier’s law equation, three cases are presented;
with fractional spatial derivative, fractional temporal
derivative and fractional space-time derivative (both
derivatives in simultaneous form). In this analysis we introduce
fractional dimensional parameters σx and σt with
dimensions of meters and seconds respectively. The fractional
derivative of Caputo type is considered and the analytical
solutions are given in terms of the Mittag-Leffler
function. The generalization of the equations in spacetime
exhibit different cases of anomalous behavior and
Non-Fourier heat conduction processes. An illustrative example
is presented.