For the work on paper, prepare new techniques by constructing a new definition called the fractional ZMA-transform (FZMAT). These techniques are used to make a solution to a fractional differential equation (FDE) easier by employing fractional analysis through the Riemann-Liouville (R-L) derivative. Also proposed attractive details and studied the relationship between the ZMA-transform (ZMAT) and the Laplace transform (LT). Moreover, present some applications for solving first and second order (1st and 2nd) linear fractional differential Equations (LFDEs).