4 citations · 8 across the 4 of their papers we have counts for
5 papers
Symmetrical Sonin kernels in terms of the hypergeometric functions
Yuri Luchko
In this paper, we introduce a new class of the kernels of the integral transforms of the Laplace convolution type that we call symmetrical Sonin kernels. For a symmetrical Sonin ke…
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations
Yuri Luchko, Masahiro Yamamoto
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differentia…
Comparison principles for the linear and semiliniar time-fractional diffusion equations with the Robin boundary condition
Yuri Luchko, Masahiro Yamamoto
The main objective of this paper is analysis of the initial-boundary value problems for the linear and semilinear time-fractional diffusion equations with a uniformly elliptic spat…
The 1st Level General Fractional Derivatives and some of their Properties
Yuri Luchko
In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far. These are integro-d…
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…