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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 * α y(t)=f(t,y(t),D * β 1 y(t),,D * β n y(t)),y (k) (0)=c k ,k=0,,m,

where m<αm+1, 0<β 1 <β 2 <<β n <α and D * α denotes Caputo fractional derivative of order α 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.

65R20Integral equations (numerical methods)
26A33Fractional derivatives and integrals (real functions)
45G10Nonsingular nonlinear integral equations
45J05Integro-ordinary differential equations