Laplace transform method for solving ordinary fractional order differential equations with constant coefficients. +CD

Fractional Calculus is a branch of mathematical analysis that satisfies
the possibility of considering the power of the differential operator as a real number. Several different families of fractional derivatives (such as, Riemann_Liouville, Caputo, Hadamard and others) are developed. In this work, we are investigate the applications of the Laplace transform to construct the solution of homogenous and nonhomogeneous linear differential equations having multi_arbitrary fractional order derivatives involving the Riemann_Liouville fractional derivatives with constant coefficients in terms of special function called _Mittage_Leffler Function_ by using Laplace transform formula for such special function and their derivatives. Several examples are solved to demonstrate our constructed solutions formulas .