390 documents found, page 1 of 39
Analytical stability analysis of the fractional-order particle swarm optimizati...
Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Machado, J. A. TenreiroMathematical modeling plays an important role in biology for describing the dynamics of infectious diseases. A useful strategy for controlling infections and disorder conditions is to adopt computational algorithms for determining interactions among their processes. The use of fractional order (FO) calculus has been proposed as one relevant tool for improving heuristic models. The particles memory is captured b...
Analysis of dual Bernstein operators in the solution of the fractional convecti...
Sayevand, K.; Machado, J. A. Tenreiro; Masti, I.The Bernstein operators (BO) are not orthogonal, but they have duals, which are obtained by a linear combination of BO. In recent years dual BO have been adopted in computer graphics, computer aided geometric design, and numerical analysis. This paper presents a numerical method based on the Bernstein operational matrices to solve the time–space fractional convection–diffusion equation. A generalization of the ...
Design of multi innovation fractional LMS algorithm for parameter estimation of...
Chaudhary, Naveed Ishtiaq; Raja, Muhammad Asif Zahoor; He, Yigang; Khan, Zeshan Aslam; Machado, J. A. TenreiroThe development of procedures based on fractional calculus is an emerging research area. This paper presents a new perspective regarding the fractional least mean square (FLMS) adaptive algorithm, called multi innovation FLMS (MIFLMS). We verify that the iterative parameter adaptation mechanism of the FLMS uses merely the current error value (scalar innovation). The MIFLMS expands the scalar innovation into a v...
Multidimensional scaling and visualization of patterns in distribution of nontr...
Machado, J. A. Tenreiro; Luchko, YuriIn this paper, we analyze the nontrivial zeros of the Riemann zeta-function using the multidimensional scaling (MDS) algorithm and computational visualization features. The nontrivial zeros of the Riemann zeta-function as well as the vectors with several neighboring zeros are interpreted as the basic elements (points or objects) of a data set. Then we employ a variety of different metrics, such as the Jeffreys ...
Optimal solution of the fractional order breast cancer competition model
Hassani, H.; Machado, J. A. Tenreiro; Avazzadeh, Z.; Safari, E.; Mehrabi, S.In this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess est...
Uniform Manifold Approximation and Projection Analysis of Soccer Players
Lopes, António M.; Machado, J. A. TenreiroIn professional soccer, the choices made in forming a team lineup are crucial for achieving good results. Players are characterized by different skills and their relevance depends on the position that they occupy on the pitch. Experts can recognize similarities between players and their styles, but the procedures adopted are often subjective and prone to misclassification. The automatic recognition of players’ ...
An efficient local meshless approach for solving nonlinear time-fractional four...
Nikan, O.; Avazzadeh, Z.; Machado, J. A. TenreiroThis paper adopts an efficient meshless approach for approximating the nonlinear fractional fourth-order diffusion model described in the Riemann–Liouville sense. A second-order difference technique is applied to discretize temporal derivatives, while the radial basis function meshless generated the finite difference scheme approximates the spatial derivatives. One key advantage of the local collocation method ...
Numerical study of the nonlinear anomalous reaction–subdiffusion process arisin...
Nikan, O.; Avazzadeh, Z.; Machado, J. A. TenreiroThis paper presents a meshless method based on the finite difference scheme derived from the local radial basis function (RBF-FD). The algorithm is used for finding the approximate solution of nonlinear anomalous reaction–diffusion models. The time discretization procedure is carried out by means of a weighted discrete scheme covering second-order approximation, while the spatial discretization is accomplished ...
Complex-order particle swarm optimization
Machado, J. A. Tenreiro; Abedi Pahnehkolaei, Seyed Mehdi; Alfi, AlirezaIn this paper, the generalization of the Particle Swarm Optimization (PSO) algorithm is proposed. The new algorithm involves the adoption of complex-order derivatives (CD). Since the CD produce complex-valued results, conjugate pairs of CD are considered for designing the Complex-Order PSO (CoPSO). First, an extensive sensitivity analysis is carried out for studying the influence of the control parameters on th...
Entropy analysis of human death uncertainty
Machado, J. A. Tenreiro; Lopes, António M.Uncertainty about the time of death is part of one’s life, and plays an important role in demographic and actuarial sciences. Entropy is a measure useful for characterizing complex systems. This paper analyses death uncertainty through the concept of entropy. For that purpose, the Shannon and the cumulative residual entropies are adopted. The first may be interpreted as an average information. The second was pr...