Convolution-to-sum identities are derived for Mittag-Leffler type functions R_alpha,v and P_alpha,w, reducing convolutions to finite sums of the same functions when their orders are rationally related.
Pure Appl
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Fractional viscoelastic rough contact models reproduce logarithmic aging but erase prior memory and lack any decreasing contact area phase after unloading; this holds for all linear viscoelastic models, requiring additional local internal variables.
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Convolution-to-sum identities for Mittag-Leffler type functions
Convolution-to-sum identities are derived for Mittag-Leffler type functions R_alpha,v and P_alpha,w, reducing convolutions to finite sums of the same functions when their orders are rationally related.
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Evolution of the contact between rough viscoelastic solids after decreasing loads: memory erasure and monotonic increase
Fractional viscoelastic rough contact models reproduce logarithmic aging but erase prior memory and lack any decreasing contact area phase after unloading; this holds for all linear viscoelastic models, requiring additional local internal variables.