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If ψ ∈ F n, we will write Ψ ( t ) = ψ ( t, t, …, t ) (obviously, this function belongs to F 1 ).
This function belongs to the family of Mittag Feffler's-type functions, which he developed already in the early 20th century [32].
The continuous function (alpha: [0, a rightarrow[0, infty)) belongs to class κ if it strictly is increasing and (alpha (0)=0). This function belongs to (kappa_{infty}) if (a=infty) and with r increasing to infinity, (a(r)) also tends to infinity.
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If, then the function belongs to.
Therefore the function belongs to the space.
Then if and only if and the function belongs to.
Let be a function in, from Lemma 2.4 the function belongs to.
is a continuous function such that the function belongs to whenever and.
Moreover, one can easily verify that the function belongs to if and only if.
Moreover, if and, then the function belongs to and the following estimate holds: (2.19).
Also, for all and, the function belongs to for some constant.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com