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- Technische Universität BerlinDE7 papers
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- Istituto Nazionale di Fisica Nucleare, Sezione di BolognaIT2 papers
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5 papers · 1 filter
Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation
Yuri Luchko
This paper is devoted to an in deep investigation of the first fundamental solution to the linear multi-dimensional space-time-fractional diffusion-wave equation. This equation is…
On the maximum principle for a time-fractional diffusion equation
Yuri Luchko, Masahiro Yamamoto
In this paper, we discuss the maximum principle for a time-fractional diffusion equation $$ \partial_t^αu(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_j u(x,t)) + c(x)u(x,t)…
Cauchy and signaling problems for the time-fractional diffusion-wave equation
Yuri Luchko, Francesco Mainardi
In this paper, some known and novel properties of the Cauchy and signaling problems for the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional deriv…
Operator theoretic approach to the Caputo derivative and the fractional diffusion equations
Rudolf Gorenflo, Yuri Luchko, Masahiro Yamamoto
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fracti…
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
Yuri Luchko
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximu…