Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method. (English) Zbl 1102.65136

Summary: We use the Adomian decomposition method for solving the fractional nonlinear two-point boundary value problem \[ D^\alpha u(x)+\mu F\bigl (x,u(x)\bigr)=0,\quad 0<x<1,\;1<\alpha\leq 2, \]
\[ u(0)=0,\;u(1)=c, \] 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.


65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
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