Analytical approximate solutions for nonlinear fractional differential equations. (English) Zbl 1029.34003

Summary: We consider a class of nonlinear fractional-differential equations bsed on the Caputo fractional derivative and, by extending the application of the Adomian decomposition method, we derive an analytical solution in the form of a series with easily computable terms. For linear equations, the method gives an exact solution, and, for nonlinear equations, it provides an approximate solution with good accuracy. Several examples are discussed.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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