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- 저자 : C.-A. Cruz-Lopez (검색결과 1 건)
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Fractional Radioactive Decay Law and Bateman equations
C.-A. Cruz-Lopez,G. Espinosa-Paredes 한국원자력학회 2022 Nuclear Engineering and Technology Vol.54 No.1
The aim of this work is to develop the fractional Bateman equations, which can model memory effects insuccessive isotopes transformations. Such memory effects have been previously reported in the alpha decay,which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alphadecays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations,which can reproduce the standard ones when the fractional order is equal to one. The proposed fractionalmodel preserves the mathematical shape and the symmetry of the standard equations, being the onlydifference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a veryimportant result, because allows the implementation of the proposed fractional model in burnup and activationcodes in a straightforwardway.Numerical experiments showthat the proposed equations predict highdecay rates for small timevalues, in comparisonwith the standard equations,which have high decay rates forlarge times. This work represents a novelty approach to the theory of successive transformations, and opensthe possibility to study properties of the Bateman equation from a fractional approach
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