arXiv subjects

Donatella Bongiorno

Publications and source records attributed to Donatella Bongiorno.

5 recordsLinked to original sources

arXiv2024

Second $α$-Order Fractal Differential Equations

In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a second $α$-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for second $α$-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for second $α$-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation.

math.GM↗

arXiv2024

On Homogeneous System of Fractal Differential Equations

In this paper, a homogeneous system of n $α$-order linear fractal differential equation is defined and the set of its fundamental solutions through the corresponding Wronskian matrix is described. Finally, the solutions of some assigned autonomous homogeneous system are plotted to show the details previously proved.

math.GM↗

arXiv2023

Solving and Applying Fractal Differential Equations: Exploring Fractal Calculus in Theory and Practice

In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for solving $α$-order differential equations. Notably, we extend our analysis to solve Fractal Bernoulli differential equations. The applications of our findings are then showcased through the solutions of problems such as fractal compound interest, the escape velocity of the earth in fractal space and time, and estimation of time of death incorporating fractal time. Visual representations of our results are also provided to enhance understanding.

math.GM↗

arXiv2021

Uniform convergence for sequences of best L^{p} approximation

Let $f$ be a continuous monotone real function defined on a compact interval $[a,b]$ of the real line. Given a sequence of partitions of $[a,b]$, $% Δ_n $, $\left\Vert {Δ}_{n}\right\Vert \rightarrow 0$, and given $l\geq 0,m\geq 1$, let $\mathbf{S}_{m}^{l}(Δ_{n}) $ be the space of all functions with the same monotonicity of $f$ that are $% Δ_n$-piecewise polynomial of order $m$ and that belong to the smoothness class $C^{l}[a,b]$. In this paper we show that, for any $m\geq 2l+1$, $\bullet$ sequences of best $L^p$-approximation in $\mathbf{S}_{m}^{l}(Δ_{n})$ converge uniformly to $f$ on any compact subinterval of $(a,b)$; $\bullet$ sequences of best $L^p$-approximation in $\mathbf{S}_{m}^{0}(Δ_{n})$ converge uniformly to $f$ on the whole interval $[a,b] $.

math.NA↗

arXiv2020

Linear Dynamics Induced by Odometers

Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing variety dynamical properties. Recently, a systematic study of dynamical properties of composition operators on $L^p$ spaces has been initiated. This class of operators includes weighted shifts and also allows flexibility in construction of other concrete examples. In this article, we study one such concrete class of operators, namely composition operators induced by measures on odometers. In particular, we study measures on odometers which induce mixing and transitive linear operators on $L^p$ spaces.

math.DS↗