Laplace Transform Method for Solving Ordinary Fractional Order Differential Equations with Constant Coefficients

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.