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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:
34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
65L05Initial value problems for ODE (numerical methods)
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