Ambra Lattanzi

Bio: Ambra Lattanzi is an academic researcher from Polish Academy of Sciences. The author has contributed to research in topics: Fractional calculus & Operator (computer programming). The author has an hindex of 4, co-authored 17 publications receiving 47 citations. Previous affiliations of Ambra Lattanzi include ENEA.

On complete monotonicity of three parameter Mittag-Leffler function

Abstract: Using the Bernstein theorem we prove the complete monotonicity of the three parameter Mittag–Leffler function Eγα,β (−w) for w ≥ 0 and suitably constrained parameters α, β and γ.

On the complete monotonicity of the three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$

Abstract: Using the Bernstein theorem we give a simple proof of the complete monotonicity of the three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$ for $x \geq 0$ and suitably adjusted parameters $\alpha$, $\beta$ and $\gamma$

Dual Numbers and Operational Umbral Methods

Abstract: Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view, embedding dual numbers within a formalism reminiscent of operational umbral calculus.

Quantum electrodynamics

Abstract: THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

The Operational Calculus

Abstract: AT the thirtieth meeting of the Indian Science Congress, held at Calcutta during January 2-4, Dr. S. C. Dhar, president of the Section of Mathematics and Statistics, discussed certain developments of mathematics in. the last thirty years. Mathematical research is now so varied that it is difficult for an active worker in one branch to follow progress in other branches. It is, therefore, very valuable when a specialist can give an intelligible summary of the chief results obtained, in some particular subject. Dr. Dhar selected “Operational Calculus and Auto-morphic Functions”. In what appears below, Dr. Dhar's address has been supplemented by matter obtained from other sources.

A practical guide to Prabhakar fractional calculus

Abstract: The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known as the Prabhakar function. Specifically, after reviewing key historical events that led to the discovery and modern development of this peculiar function, we discuss how the latter allows one to introduce an enhanced scheme for fractional calculus. Then, we summarize the progress in the application of this new general framework to physics and renewal processes. We also provide a collection of results on the numerical evaluation of the Prabhakar function.