Author
Carlo Cattani
Other affiliations: Akdeniz University, University of Salerno, Sapienza University of Rome ...read more
Bio: Carlo Cattani is an academic researcher from Tuscia University. The author has contributed to research in topics: Wavelet & Fractional calculus. The author has an hindex of 42, co-authored 308 publications receiving 5804 citations. Previous affiliations of Carlo Cattani include Akdeniz University & University of Salerno.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the authors used the Bernstein wavelet and Euler method to solve a nonlinear fractional predator-prey biological model of two species and compared the capability of the two methods.
Abstract: In this endeavour, Bernstein wavelet and Euler methods are used to solve a nonlinear fractional predator-prey biological model of two species. The theoretical results with their corresponding biological consequence due to Bernstein wavelet are considered and discussed. A test problem of predator-prey model with two different cases are examined to determined the capability of our proposed methods. We showed that the obtained solutions are the most powerful and, wherever it is possible the comparison, in a very good coincidence with the other numerical solution. Few numerical simulations are finding for predator and prey populations and new chaotic behaviours of predator-prey population model are also obtained by using the Euler method. Moreover, a comparison have been done between the capability of the Bernstein wavelet and the Euler approach. The numerical simulations and behaviours of Rabies model are depicted through graphically which is a special case of predator-prey model.
200 citations
TL;DR: It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
Abstract: This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
185 citations
01 Jan 2020
TL;DR: In this paper, a conformable (2+1)-dimensional Ablowitz-KaupNewell-Segur equation is studied and the existence of complex combined dark-bright soliton solutions is shown.
Abstract: In this paper, we study on the conformable (2+1)-dimensional Ablowitz-KaupNewell-Segur equation in order to show the existence of complex combined dark-bright soliton solutions. To this purpose an effective method which is the sine-Gordon expansion method is used. The 2D and 3D surfaces under some suitable values of parameters are also plotted.
156 citations
137 citations
TL;DR: From the fractal electrodynamics point of view, the relaxation oscillator, defined on Cantor sets in LC-electric circuit, and its exact solution using the local fractional Laplace transform are obtained.
137 citations
Cited by
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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …
33,785 citations
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.
2,446 citations
07 Aug 2002
TL;DR: In this paper, the authors describe decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks, which are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies.
Abstract: This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.
2,445 citations
2,345 citations
Posted Content•
TL;DR: This paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies which are adaptive, distributed, asynchronous, and verifiably correct.
Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.
2,198 citations