371 citations · 589 across the 56 of their papers we have counts for
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Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables
Alexandra V. Antoniouk, Andrei Yu. Khrennikov, Anatoly N. Kochubei
We study the Cauchy problem for -adic nonlinear evolutionary pseudo-differential equations for complex-valued functions of a real positive time variable and p-adic spatial varia…
Nonlinear Pseudo-Differential Equations for Radial Real Functions on a Non-Archimedean Field
Anatoly N. Kochubei
In an earlier paper (A. N. Kochubei, {\it Pacif. J. Math.} 269 (2014), 355--369), the author considered a restriction of Vladimirov's fractional differentiation operator , $α>…
Growth Equation of the General Fractional Calculus
Anatoly N. Kochubei, Yuri Kondratiev
We consider the Cauchy problem , , where is the general convolutional derivative introduced in the paper (A. N. Kochubei, In…
Representations of the Infinite-Dimensional -Adic Affine Group
Anatoly N. Kochubei, Yuri Kondratiev
We introduce an infinite-dimensional -adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for…
Heat Kernel Estimates for Fractional Heat Equation
Anatoly N. Kochubei, Yuri G. Kondratiev, José L. da Silva
We study the long-time behavior of the Cesaro means of fundamental solutions for fractional evolution equations corresponding to random time changes in the Brownian motion and othe…
Random Time Change and Related Evolution Equations: Time Asymptotic Behavior
Anatoly N. Kochubei, Yuri Kondratiev, José L. da Silva
In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We co…