  In this manuscript we introduced the generalized fractional Riemann-Liouville
and Caputo like derivative for functions defined on fractal sets. The Gamma,
Mittag-Leffler and Beta functions were defined on the fractal sets. The
non-local Laplace transformation is given and applied for solving linear and
non-linear fractal equations. The advantage of using these new nonlocal
derivatives on fractals subset of real-line lies in the fact that they are used
for better modelling of processes with memory effect.
