Solving a multi-order fractional differential equation using adomian decomposition

An algorithm has been developed to convert the multi-order fractional differential equation:D∗αy(t)=f(t,y(t),D∗β1y(t),…,D∗βny(t)),y(k)(0)=ck,k=0,…,m,where m < α ⩽ m + 1, 0 < β1 < β2 < ⋯ < βn < α   and D∗α denotes Caputo fractional derivative of order α into a system of fractional differential equations. Further Adomian decomposition method has been employed to solve the system of fractional differential equations. Some illustrative examples are presented.