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MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversaryThis 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 and its applications...
We discuss functions f : X × Y → Z such that sets of the form
f (A × B) have non-empty interiors provided that A and B are non-empty
sets of second category and have the Baire property.
Considering jets, or functions, belonging to some strongly non-quasianalytic Carleman class on compact subsets of , we extend them to the whole space with a loss of Carleman regularity. This loss is related to geometric conditions refining Łojasiewicz’s “regular separation” or Whitney’s “property (P)”.
By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus...
In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic -mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic -mild solution of a two-dimensional impulsive fractional...
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