  Many possible definitions have been proposed for fractional derivatives and
integrals, starting from the classical Riemann-Liouville formula and its
generalisations and modifying it by replacing the power function kernel with
other kernel functions. We demonstrate, under some assumptions, how all of
these modifications can be considered as special cases of a single, unifying,
model of fractional calculus. We provide a fundamental connection with
classical fractional calculus by writing these general fractional operators in
terms of the original Riemann-Liouville fractional integral operator. We also
consider inversion properties of the new operators, prove analogues of the
Leibniz and chain rules in this model of fractional calculus, and solve some
fractional differential equations using the new operators.
