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...
2000 Mathematics Subject Classification: 35A15, 44A15, 26A33
The paper is devoted to the study of the Cauchy-type problem for the
differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.
2000 Mathematics Subject Classification: 33C60, 33C20, 44A15
The paper is devoted to the study of the function Zνρ(x) defined for
positive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0
for ρ ≤ 0, [...]
Such a function was earlier investigated for ρ > 0. Using the Mellin transform
of Zνρ(x), we establish its representations in terms of the H-function
and extend this function from positive x > 0 to complex z. The results
obtained, being different for ρ >...
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