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• W4313362443 abstract "For the impulsive fractional-order system (IFrOS) of order ϵ∈(1,2), there have appeared some conflicting equivalent integral equations in existing studies. However, we find two fractional-order properties of piecewise function and use them to verify that these given equivalent integral equations have some defects to not be the equivalent integral equation of the IFrOS. For the IFrOS, its limit property shows the linear additivity of the impulsive effects. For the IFrOS, we use the limit analysis and the linear additivity of the impulsive effects to find its correct equivalent integral equation, which is a combination of some piecewise functions with two arbitrary constants; that is, the solution of the IFrOS is a general solution. Finally, a numerical example is given to show the equivalent integral equation and the non-uniqueness of the solution of the IFrOS." @default.
• W4313362443 created "2023-01-06" @default.
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• W4313362443 date "2022-12-29" @default.
• W4313362443 modified "2023-10-17" @default.
• W4313362443 title "The Right Equivalent Integral Equation of Impulsive Caputo Fractional-Order System of Order ϵ∈(1,2)" @default.
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• W4313362443 doi "https://doi.org/10.3390/fractalfract7010037" @default.
• W4313362443 hasPublicationYear "2022" @default.
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