Carlo Cattani

University of Tuscia | Tuscia · Department of Economics, Engineering, Society and Business Organization - DEIM

In this paper, the distribution of primes and prime-indexed primes (PIPs) is studied by mapping primes into a binary image which visualizes the distribution of primes. These images show that the distribution of primes (and PIPs) is similar to a Cantor dust, moreover the self-similarity with respect to the order of PIPs (already proven in [3]) can b...

In this article, we propose and apply a local fractional homotopy perturbation method, which is and extended form of the classical homotopy perturbation method. We discuss convergence aspect of the technique and present two illustrative examples to show the efficiency of the proposed method in order to find the approximate solutions for some local...

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô-Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, su...

Shannon wavelets are studied together with their differential properties (known as connection coefficients). It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of functions....

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is pleased to present Volume 2, Issue 2, featuring a carefully curated collection of eight research articles that contribute to the development of applied mathematics and scientific computing. This issue reflects the journal’s steadfast dedication to fostering schola...

In this paper, we provide a brief review of fractal calculus. We introduce the fractal telegraph equation, which generalizes both the fractal heat and wave equations, and derive its solution. The solutions are plotted to highlight the differences between fractal differential equations and standard differential equations, demonstrating the effects o...

The sun is a fundamental element of the natural environment, and kinetic equations are crucial mathematical models for determining how quickly the chemical composition of a star like the sun is changing. Taking motivation from these facts, we develop and solve a novel fractional kinetic equation containing Fermi–Dirac (FD) and Bose–Einstein (BE) fu...

The Second International Conference on Mathematical Analysis, Applications and Computational Simulation (2024 ICMAACS) is aimed to provide a high-level platform where mathematicians and scientists exchange recent developments, discoveries, and progress in Pure and Applied Mathematics and Their Applications in real-world problems. Its aim is to crea...

In this paper, we introduce Fractal Volterra Integral Equations and Fractal Fredholm Integral Equations. We derive the corresponding fractal differential equations and provide solutions to several examples. As an application, we solve the fractal linear oscillator equation and plot its solution to illustrate the impact of fractal support on the res...

In this paper, we introduce fractal volterra integral equations and fractal Fredholm integral equations. We derive the corresponding fractal differential equations and provide solutions to several examples. As an application, we solve the fractal linear oscillator equation and plot its solution to illustrate the impact of fractal support on the res...

Mathematics, mathematical modeling of real systems, and mathematical and computer methodologies aimed at the qualitative and quantitative study of real physical systems interact in a nontrivial way. This work aims to examine a new class of inverse problems for a fractional partial differential equation with order fractional 0<ρ≤1$$ 0<\rho \le 1 $$,...

In this paper, we first summarize fractal calculus and extend Itô calculus to fractal sets, focusing on the integration and differentiation of stochastic processes within fractal structures. We compare Brownian motion on the real line with that on a ternary Cantor set, generalizing Itô's framework to accommodate fractal geometry complexities. We de...

In this paper, we provide a summary of fractal calculus and propose the use of Lagrangian multipliers for fractal calculus and fractal variational calculus with constraints. We explore the application of these methods across various branches of physics. By utilizing fractal variational calculus with constraints, we derive key equations such as the...

This paper provides a comprehensive study of fractal calculus and its application to differential equations within fractal spaces. It begins with a review of fractal calculus, covering fundamental definitions and measures related to fractal sets. The necessary preliminaries for understanding fractal Green's functions are introduced, laying the grou...

Measles has emerged as one of the leading causes of child mortality globally, leading to an estimated 142,300 fatalities annually, despite the existence of a reliable and safe vaccine. Moreover, a surge in global measles cases has occurred in recent years, predominantly among children below 5 years old and immunocompromised adults. The escalating i...

In this paper, we provide a brief overview of fractal calculus and present a comprehensive study of the calculus of variations for functionals on fractal sets. We begin by introducing the calculus of variations for functionals with several dependent variables on fractal sets. We then explore the calculus of variations for functionals with several i...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is a peer-reviewed, open-access international journal, published semiannually by the University Center Abdelhafid Boussouf in Mila, Algeria. JIAMCS is dedicated to disseminating high-quality original research and comprehensive review articles across various fields, in...

In this paper, we consider the Schrödinger-Pauli problem on a finite square domain. Because of the boundary conditions we have proposed as a solution a suitable trigonometric series. We have shown that these coefficients exist and can be univocally determined by solving a simple algebraic system. Mathematics Subject Classification. 35Q40, 35N05, 81...

Self-similarity is a common feature among mathematical fractals and various objects of our natural environment. Therefore, escape criteria are used to determine the dynamics of fractal patterns through various iterative techniques. Taking motivation from this fact, we generate and analyze fractals as an application of the proposed Mann iterative te...

A numerical scheme based on the Haar wavelets coupled with the nonstandard finite difference scheme is presented to solve the variable-order time-fractional generalized Burgers’ equation (VO-TFGBE). In the proposed technique, firstly, we approximate the time-fractional derivative by the nonstandard finite difference (NSFD) scheme and convert the VO...

The chapter is concerned with the development of a wavelet based study to understanding the anisotropic (directional) behavior of images, especially nanoimages and oscillations in nanomaterials. Wavelets are nowadays sophisticated tools in image processing permitting to explain many complicated cases of images such as nano, bio, and also the mixed...

Fractal geometry plays an important role in the description of the characteristics of nature. Local fractional calculus, a new branch of mathematics, is used to handle the non-differentiable problems in mathematical physics and engineering sciences. The local fractional inequalities, local fractional ODEs and local fractional PDEs via local fractio...

Dear Colleagues, This is a call for articles for the Special Issue on Computational Linguistics and Artificial Intelligence. The editor Mr. Addison Su proposes to get discounts on submission (the deadline is November 30, 2024). https://www.mdpi.com/journal/sci/special_issues/computational_linguistics_and_artificial_intelligence Kind regards, Dion...

Accurate prediction of photovoltaic (PV) power generation is the key to daily dispatch management and safe and stable grid operation. In order to improve the accuracy of the prediction, a finite iterative PV power prediction model with long range dependence (LRD) characteristics was developed using fractional Lévy stable motion (fLsm) and applied t...

In this study, we take an approach to the development of sustainable or consistent economic models, which is described through the interactions between political discourse and economics. We highlight the importance of language in both-political discourse and economy-, as an articulating element from real to monetary factors, and the indescribable c...

The integration of physical and cybernetic systems introduces new functionalities that modify the configuration of autonomous driving vehicles. The vehicle's driving behavior is subject to respond differently than the driver expects, causing accidents. Innovation in cybernetic systems is based on still immature information. To achieve socially resp...

The integration of physical and cybernetic systems introduces new functionalities that modify the configuration of autonomous driving vehicles. The vehicle's driving behavior is subject to respond differently than the driver expects, causing accidents. Innovation in cybernetic systems is based on still immature information. To achieve socially resp...

Dear Colleagues, There is growing concern in physics, biology, bioengineering, and medicine about models that explain the complex functioning of the brain. There are already basic elements necessary for modeling promising intelligent systems, such as deterministic computational models and artificial intelligence, AI, and algorithms. These models a...

In this paper, we consider the Schrödinger–Pauli problem on a finite square domain. Because of the boundary conditions we have proposed as a solution a suitable trigonometric series. We have shown that these coefficients exist and can be univocally determined by solving a simple algebraic system.

This paper deals with the option pricing in the illiquid markets under the mixed fractional geometric Brownian motion model with jump process. We propose a general long memory financial model, where its featuring parameters are related to demand and supply by showing also the existence of some restrictions on them. Moreover, by using the delta Hedg...

The paper introduces a novel probability descriptor for genome sequence comparison, employing a generalized form of Jensen-Shannon divergence. This divergence metric stems from a one-parameter family, comprising fractions up to a maximum value of half. Utilizing this metric as a distance measure, a distance matrix is computed for the new probabilit...

To solve fractional partial differential equations (FPDEs) under various physical conditions, this study developed a novel method known as the Hermite wavelet method employing the functional integration matrix. The method that has been suggested is based on the Hermite wavelet collocation process. To determine the solution of the fractional differe...

The approach that leads to the development of sustainable economic models is described through the interactions of political discourse in the economy. We highlight the importance of both language as an articulating element from real factors to monetary factors, and the indescribable characteristic of value, as something that is integrated into the...

In this study, the Atangana–Baleanu fractional derivative in the Caputo type (as a kind of non‐local and non‐singular derivative) is used to define a new class of stochastic fractional integro‐differential equations. A projection method (more precisely, a Galerkin approach) based on the piecewise Chebyshev cardinal functions is developed to solve t...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open-access, peer-reviewed semiannual international journal published by the Abdelhafid Boussouf University Center of Mila, Algeria. The journal publishes high-quality original research and review papers from various fields related to applied mathematics,...

The graph model is an appreciable tool for data transmission network, where the feasibility of data transmission in site attack circumstances can be described by fractional critical graphs, and the vulnerability of networks can be measured by isolation toughness variant. This paper considers both the stability of the network and the feasibility of...

This article shows that the unambiguous meaning representation of machine language must be inspired by human cognition to find a universal label for Natural Language Processing resources. We show, that the meaning representation is linked to the quality and not to the quantity of data, since the architecture of human symbolization, taken as a model...

The graph model is an appreciable tool for data transmission network, where the feasibility of data transmission in site attack circumstances can be described by fractional critical graphs, and the vulnerability of networks can be measured by isolation toughness variant. This paper considers both the stability of the network and the feasibility of...

To solve the fractional gas dynamic equation, this paper presents an effective algorithm using the collocation method and Müntz-Legendre (M-L) polynomials. The approach chooses a solution of a finite-dimensional space that satisfies the desired equation at a set of collocation points. The collocation points in this study are selected to be uniforml...

We investigate the behavior of a complex three-strain model with a generalized incidence rate. The incidence rate is an essential aspect of the model as it determines the number of new infections emerging. The mathematical model comprises thirteen nonlinear ordinary differential equations with susceptible, exposed, symptomatic, asymptomatic and rec...

In this article, we solve a class of coupled systems of nonlinear differential equations with appropriate initial, boundary, and four-point boundary conditions. We use quasilinearization to linearise these systems of equations and then use the Haar wavelets collocation approach to get the numerical solutions. We propose three quasilinearization sch...

We define a new class of linear canonical wavelet transform (LCWT) and study its properties like inner product relation, reconstruction formula and also characterize its range. We obtain Donoho-Stark's uncertainty principle for the LCWT and give a lower bound for the measure of its essential support. We also give the Shapiro's mean dispersion theor...

2023 The International Conference on Mathematical Analysis, Applications and Computational Simulation (ICMAACS 2023) is aimed to provide a high-level platform where mathematicians and scientists exchange recent developments, discoveries, and progress in Pure and Applied Mathematics and Their Applications in real-world problems. Its aim is to create...

This paper focuses on the classification of forest biomass into two categories: premature and mature forest biomass. The third variable considered is industrialization. The growth of the wood-based industry is believed to be closely tied to the population of mature forest biomass. Any scarcity of the mature population could have a negative impact o...

In this paper, we derive some classical and fractional properties of the rRs matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss hypergeometric matrix functions. We will also show the relationshi...

In this article, we study the fractional SIR epidemic model with the Atangana–Baleanu–Caputo fractional operator. We explore the properties and applicability of the ZZ transformation on the Atangana–Baleanu–Caputo fractional operator as the ZZ transform of the Atangana–Baleanu–Caputo fractional derivative. This study is an application of two power...

Synopsis Mathematics plays an important role in the linguistic structure of artificial intelligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfer...

Due to the exponential growth of big data, collecting and analyzing irregular, noisy, and complex datasets have become increasingly common across various fields, such as physics, engineering, and finance. To address this challenge, chaotic and fractal models have become valuable tools for characterizing various data types exhibiting patterns simila...

The study of the complex model associated with chaotic models is always the most complicated and fundamental in the current scientific environment. The primary goal of the current paper is to provide an illustration of the fundamental theory while analysing dynamical systems and validating the chaotic behaviour of the Lorenz–Haken (LH) equations, a...

As a volunteer Collaborating Researcher at the Engineering school department DEIM, University of Tuscia, since 2019 and under the supervision of Professor Carlo Cattani, we have, as a result of the joint project “Natural language of Artificial Intelligence”: papers on international peer review journals and a book.

This paper deals with the existence of many solutions a degenerate weighted elliptic equation which its the number of solutions depend on degeneracy term a i.e., the number of subdomains of Ω\a⁻¹(0) whose boundary is made by submanifolds with 1-codimension. Moreover, by the Ljusternik-Schnirelman principle, we would study the corresponding eigenval...

The paper exhibits a practical and effective scheme to approximate the solutions of a class of fractional differential equations known as the Bagley-Torvik equations. The underlying fractional derivative is based on the Caputo definition. Both the boundary and initial conditions are considered while the domain of approximation is taken sufficiently...

Detrended fluctuation analysis considers single statistical series and studied possible fluctuations in time by estimating scaling exponents, dynamics, etc. However, in many cases it is necessary to consider simultaneously many series and study their behavior once. This leads to the extension of detrended fluctuation analysis to mixed detrended flu...

In this paper, an adaptive remaining useful life prediction model is proposed for electric vehicle lithium batteries. Capacity degradation of the electric car lithium batteries is modeled by the multi-fractal Weibull motion. The varying degree of long-range dependence and the 1/f characteristics in the frequency domain are also analyzed. The age an...

Due to numerous biomedical information-sensing devices, such as Computed Tomography (CT), Magnetic Resonance (MR) Imaging, Ultrasound, Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET), Magnetic Particle Imaging, EE/MEG, Optical Microscopy and Tomography, Photoacoustic Tomography, Electron Tomography, and Atomic...

Call for papers: The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) calls scholars, academics, scientists, and researchers worldwide to submit their original papers for inclusion in our upcoming issue (Volume: 03, Issue: 01, January to June 2023). JIAMCS welcomes high-quality original research papers in all areas of...

We propose two efficient numerical algorithms, Bernoulli uniform collocation method and Bernoulli Chebyshev collocation method}for solving third-order Lane-Emden-Fowler boundary value problems. To avoid singularity at $x=0$, we transform the concerned problem into its integral form. By using the Bernoulli collocation method, the resulting integral...

For three-point Lane-Emden-Fowler boundary value problems (LEFBVPs), we propose two robust algorithms consisting of Bernstein and shifted Chebyshev polynomials coupled with the collocation technique. The first algorithm uses the Bernstein collocation method with uniform collocation points, while the second is based on the shifted Chebyshev collocat...

In the present study, the effects of the strong Allee effect on the dynamics of the modified Leslie-Gower predator-prey model, in the presence of nonlinear prey-harvesting, have been investigated. In our findings, it is seen that the behaviors of the described mathematical model are positive and bounded for all future times. The conditions for the...

Education is associated with the political responsibility of specialized institutions, whose representative, as a research advisor, is assigned the function of mediating positive and negative aspects of the use of artificial intelligence by appreciating the values at stake. Artificial intelligence, AI, is associated with the debate about its effect...

The COVID-19 pandemic still gains the attention of many researchers worldwide. Over the past few months, China faced a new wave of this pandemic which increases the risk of its spread to the rest of the world. Therefore, there has become an urgent demand to know the expected behavior of this pandemic in the coming period. In this regard, there are...

In this study, we introduce a new kind of nonlinear Bernstein-Chlodowsky operators based on q-integers. Firstly, we define the nonlinear q−Bernstein-Chlodowsky operators of max-product kind. Then, we give an error estimation for the q−Bernstein Chlodowsky operators of max-product kind by using a suitable generalizition of the Shisha-Mond Theorem. T...

In this paper, we analyse the accuracy of the Haar wavelet approximation method on the singular boundary value problem. We propose to solve some higher-order nonlinear singular BVPs. We also verify that numerically the estimated order of convergence is in agreement with the obtained theoretical results.

Because of noise interference, improper exposure, and the over thickness of human tissues, the detailed information of DR (digital radiography) images can be masked, including unclear edges and reduced contrast. An image-enhancement algorithm based on wavelet multiscale decomposition is proposed to address the shortcomings of existing single-scale...

This paper is devoted to an innovative and efficient technique for solving space–time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that the bases used are interpolating scaling functions (ISFs). The operational metrics for the derivative operator and fractional integration operator are used to introduce the...

We propose a numerical scheme based on the Galerkin method for solving the time-fractional partial differential equations. To this end, after introducing the Chebyshev cardinal functions (CCFs), using the relation between fractional integral and derivative, we represent the Caputo fractional derivative based on these bases and obtain an operational...

The Language Conceptual Formation to Inspire Intelligent Systems https://www.mdpi.com/2413-4155/4/4/42 or https://www.mdpi.com/journal/sci/special_issues/computational_linguistic_and_artificial_intelligence Abstract The semantic web invests in systems that work collaboratively. In this article we show that the collaborative way is not enough, b...

This paper deals with the existence of many solutions a degenerateweighted elliptic equation which its the number of solutions dependon degeneracy term $a$ i.e., the number of subdomains of$\Omega\setminus a^{-1}(0)$ whose boundary is made by submanifoldswith 1-codimension. Moreover, by the Ljusternik–-Schnirelmanprinciple, we would study the corre...

In this article, we develop a computational technique for solving the nonlinear time-fractional one and two-dimensional partial integro-differential equation with a weakly singular kernel. For the approximation of spatial derivatives, we apply the Haar wavelets collocation method whereas, for the time-fractional derivative, we use the nonstandard f...

Engineering applications of the fractional Weibull distribution (fWd) are quite limited because a corresponding stochastic process is not yet constituted and completely analyzed of fundamental properties. In order to fill this gap, the fractional Weibull process (fWp) is defined in this paper with the realization algorithm. The self-similarity prop...

The (3 + 1)‐dimensional Vakhnenko–Parkes mathematical model has a wide range of applications in science and engineering. In this paper, the model studied is investigated and analyzed by using two effective schemes such as sine‐Gordon expansion method and its newly developed version, rational SGEM. Moreover, many novel properties of model studied ar...

Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on orthogonal polynomials as wavelets, i.e., orthogonal polynomial wavelet method (OPWM). We also discuss the convergence...

This Issue is dedicated to some selected papers of the International Conference on Mathematics and Applications (ICMA'2021), held on December 7-8, 2021, at Blida 1 University, Algeria. Guest Editor: Mohammed Hachama Associet Editors: - Benbachir Maamar -Redouane Boudjemaa ARK: https://n2t.net/ark:/49935/jiamcs.v2i2 Published: 10-09-2022

This paper introduces a new set of the basis functions called the fractional Chebyshev cardinal wavelets and details their properties. These wavelets have a greater degree of freedom than the classical Chebyshev cardinal wavelets. Moreover, they retain the cardinality and the spectral accuracy of these wavelets. The fractional derivative and integr...