2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15
The paper deals with analysis of several techniques and methods for the
numerical evaluation of the Wright function. Even if the focus is mainly on
the real arguments’ values, the methods introduced here can be used in the
complex plane, too. The approaches presented in the paper include integral
representations of the Wright function, its asymptotic expansions and
summation of series. Because the Wright function depends...
MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo
on the occasion of his 80th anniversary
In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative, the Caputo...
2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05
In the paper, the machinery of the Mellin integral transform is applied
to deduce and prove some operational relations for a general operator of the
Erdélyi-Kober type. This integro-differential operator is a composition of
a number of left-hand sided and right-hand sided Erdélyi-Kober derivatives
and integrals. It is referred to in the paper as a mixed operator of the
Erdélyi-Kober type.
For special...
2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05
The Caputo fractional derivative is one of the most used definitions of a
fractional derivative along with the Riemann-Liouville and the Grünwald-
Letnikov ones. Whereas the Riemann-Liouville definition of a fractional
derivative is usually employed in mathematical texts and not so frequently
in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional...
MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary
This paper presents a brief overview of the life story and professional
career of Prof. R. Gorenflo - a well-known mathematician, an expert in
the field of Differential and Integral Equations, Numerical Mathematics,
Fractional Calculus and Applied Analysis, an interesting conversational
partner, an experienced colleague, and a real friend. Especially his role in
the modern Fractional Calculus...
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