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A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation. (English) Zbl 1250.34006
Summary: This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method.

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems
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