Browsing by Author "Cattani, Carlo"

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Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model
(2020) Baleanu, Dumitru; Cattani, Carlo; Gomez-Aguilar, J. F.; Baleanu, Dumitru; Osman, M. S.; 56389
In this work, we introduce a numerical and analytical study of the Peyrard-Bishop DNA dynamic model equation. This model is studied analytically by hyperbolic and exponential ansatz methods and numerically by finite difference method. A comparison between the results obtained by the analytical methods and the numerical method is investigated. Furthermore, some figures are introduced to show how accurate the solutions will be obtained from the analytical and numerical methods. (C) 2020 Elsevier Ltd. All rights reserved.
Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws
(Hindawi LTD, 2014) Baleanu, Dumitru; Yang, Xiao-Jun; Baleanu, Dumitru; Cattani, Carlo; Zhao, Yang; 56389
We suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus.
Local Fractional Discrete Wavelet Transform for Solving Signals on Cantor Sets
(Hindawi LTD, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; 56389
The discrete wavelet transform via local fractional operators is structured and applied to process the signals on Cantor sets. An illustrative example of the local fractional discrete wavelet transform is given.
Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators
(Hindawi LTD, 2014) Baleanu, Dumitru; Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun; 56389
We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.
Maxwell's Equations on Cantor Sets: A Local Fractional Approach
(Hindawi LTD, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; 56389
Maxwell's equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell's equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell's equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell's equations for the dynamics of cold dark matter.
Nonlinear Dynamics of Cattaneo-Christov Heat Flux Model for Third-Grade Power-Law Fluid
(2020) Baleanu, Dumitru; Kumar, Sunil; Cattani, Carlo; Baleanu, Dumitru; 56389
A rigorous analysis of coupled nonlinear equations for third-grade viscoelastic power-law non-Newtonian fluid is presented. Initially, the governing partial differential equations for conservation of energy and momentum are transformed to nonlinear coupled ordinary differential equations using exact similarity transformations which are known as Cattaneo-Christov heat flux model for third-grade power-law fluid. The homotopy analysis method (HAM) is utilized to approximate the systematic solutions more precisely with shear-thickening, moderately shear-thinning, and most shear-thinning fluids. The solution depends on various parameters including Prandtl number, power index, and temperature variation coefficient. A systematic analysis of boundary-layer flow demonstrates the impact of these parameters on the velocity and temperature profiles.
On beta-time fractional biological population model with abundant solitary wave structures
(2022) Baleanu, Dumitru; Ciancio, Armando; Ali, Khalid K.; Osman, M.S.; Cattani, Carlo; Baleanu, Dumitru; Zafar, Asim; Raheel, M.; Azeem, M.; 56389
The ongoing study deals with various forms of solutions for the biological population model with a novel beta-time derivative operators. This model is very conducive to explain the enlargement of viruses, parasites and diseases. This configuration of the aforesaid classical scheme is scouted for its new solutions especially in soliton shape via two of the well known analytical strategies, namely: the extended Sinh-Gordon equation expansion method (EShGEEM) and the Expa function method. These soliton solutions suggest that these methods have widened the scope for generating solitary waves and other solutions of fractional differential equations. Different types of soliton solutions will be gained such as dark, bright and singular solitons solutions with certain conditions. Furthermore, the obtained results can also be used in describing the biological population model in some better way. The numerical solution for the model is obtained using the finite difference method. The numerical simulations of some selected results are also given through their physical explanations. To the best of our knowledge, No previous literature discussed this model through the application of the EShGEEM and the Expa function method and supported their new obtained results by numerical analysis.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
(Amer Inst Physics, 2016) Baleanu, Dumitru; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo
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. Published by AIP Publishing
Recent advances in computational biology
(2022) Baleanu, Dumitru; Srivastava, Hari Mohan; Cattani, Carlo; 56389
Special issue on advances in fractional dynamics in mechanical engineering
(Sage Publications LTD, 2016) Baleanu, Dumitru; Lopes, Antonio Mendes; Hristov, Jordan Yankov; Cattani, Carlo; Baleanu, Dumitru; Mohyud-Din, Syed Tauseef; 56389