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Zbl 1102.65136
Jafari, Hossein; Daftardar-Gejji, Varsha
Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method. (English)
[J] Appl. Math. Comput. 180, No. 2, 700-706 (2006). ISSN 0096-3003

Summary: We use the Adomian decomposition method for solving the fractional nonlinear two-point boundary value problem $$D^\alpha u(x)+\mu F\bigl (x,u(x)\bigr)=0,\quad 0<x<1,\ 1<\alpha\le 2,$$ $$u(0)=0,\ u(1)=c,$$ where $D^\alpha$ is Caputo fractional derivative, $c$ is a constant $\mu >0$, and $F:[0,1]\times[0,\infty) \to[0,\infty)$ a continuous function. The fractional Bratu problem is solved as an illustrative example.

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations

Keywords: numerical example; Caputo derivative; fractional Bratu equation

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