A refinement of quasilinearization method for Caputo’s sense fractional-order differential equations. (English) Zbl 1204.34011

Summary: The method of quasilinearization for fractional-order differential equationin Caputo’s sense is applied to obtain lower and upper sequences in terms of the solutions of linear fractional-order differential equations in Caputo’s sense. It is also shown that these sequences converge to the unique solution of the nonlinear fractional-order differential equation in Caputo’s sense uniformly and semiquadratically with less restrictive assumptions.


34A08 Fractional ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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