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Rapid convergence of approximate solutions for fractional differential equations. (English) Zbl 1444.34021

Summary: In this paper, we develop a generalized quasilinearization technique for a class of Caputo’s fractional differential equations when the forcing function is the sum of hyperconvex and hyperconcave functions of order \(m\) (\(m\geq 0\)), and we obtain the convergence of the sequences of approximate solutions by establishing the convergence of order \(k\) (\(k\geq 2\)).

MSC:

34A08 Fractional ordinary differential equations
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
37C60 Nonautonomous smooth dynamical systems
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