Solving a multi-order fractional differential equation using Adomian decomposition. (English) Zbl 1122.65411

Summary: An algorithm is developed to convert the multi-order fractional differential equation: \[ D^\alpha_*y(t)=f(t,y(t),D^{\beta_1}_*y(t),\dots,D^{\beta_n}_*y(t)),\quad y^{(k)}(0)=c_k,\quad k=0,\dots,m, \] where \(m<\alpha\leq m+1\), \(0<\beta_1<\beta_2<\dots<\beta_n <\alpha\) and \(D^\alpha_*\) denotes Caputo fractional derivative of order \(\alpha\) into a system of fractional differential equations. Further, the Adomian decomposition method is employed to solve the system of fractional differential equations. Some illustrative examples are presented.


65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
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