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

Daftardar-Gejji, Varsha; Jafari, Hossein

Appl. Math. Comput. 189, No. 1, 541-548 (2007).

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

Keywords:

fractional differential equation; Adomian decomposition method; Caputo fractional derivative; Riemann-Liouville fractional derivative; fractional integral; numerical examples

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