## 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.

### MSC:

 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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### References:

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