734 citations · 1.9k across the 24 of their papers we have counts for
24 papers
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…
Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann-Liouville Sense
Yuri Luchko
In this paper, we first deal with the general fractional derivatives of arbitrary order defined in the Riemann-Liouville sense. In particular, we deduce an explicit form of their n…
Special Functions of Fractional Calculus in Form of Convolution Series and their Applications
Yuri Luchko
In this paper, we first discuss the convolution series that are generated by the Sonine kernels from a class of functions continuous on the real positive semi-axis that have an int…
Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
Kai Diethelm, Virginia Kiryakova, Yuri Luchko +2
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state…