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• W2011412006 abstract "We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $${(mathbb D_{(k)} u)(t)=frac{d}{dt} int nolimits_0^tk(t-tau )u(tau ),dtau-k(t)u(0)}$$ where k is a nonnegative locally integrable function. Our results are based on the theory of complete Bernstein functions. The solution of the Cauchy problem for the relaxation equation $${mathbb D_{(k)} u=-lambda u}$$ , λ > 0, proved to be (under some conditions upon k) continuous on [0, ∞) and completely monotone, appears in the description by Meerschaert, Nane, and Vellaisamy of the process N(E(t)) as a renewal process. Here N(t) is the Poisson process of intensity λ, E(t) is an inverse subordinator." @default.
• W2011412006 created "2016-06-24" @default.
• W2011412006 creator A5041182139 @default.
• W2011412006 date "2011-10-28" @default.
• W2011412006 modified "2023-10-10" @default.
• W2011412006 title "General Fractional Calculus, Evolution Equations, and Renewal Processes" @default.
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• W2011412006 doi "https://doi.org/10.1007/s00020-011-1918-8" @default.
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