  Fractional learning algorithms are trending in signal processing and adaptive
filtering recently. However, it is unclear whether the proclaimed superiority
over conventional algorithms is well-grounded or is a myth as their performance
has never been extensively analyzed. In this article, a rigorous analysis of
fractional variants of the least mean squares and steepest descent algorithms
is performed. Some critical schematic kinks in fractional learning algorithms
are identified. Their origins and consequences on the performance of the
learning algorithms are discussed and swift ready-witted remedies are proposed.
Apposite numerical experiments are conducted to discuss the convergence and
efficiency of the fractional learning algorithms in stochastic environments.
