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- Technische Universität BerlinDE7 papers
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5 papers · 2 filters
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…
Convolution series and the generalized convolution Taylor formula
Yuri Luchko
In this paper, we deal with the convolution series that are a far reaching generalization of the conventional power series and the power series with the fractional exponents includ…
General fractional integrals and derivatives of arbitrary order
Yuri Luchko
In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable gen…
Operational Calculus for the general fractional derivatives with the Sonine kernels
Yuri Luchko
In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the poi…
General Fractional Integrals and Derivatives with the Sonine Kernels
Yuri Luchko
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. Firs…