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Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem

100%
Evirgen F.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 3
1066-1069
EN
A conformable fractional gradient based dynamic system with a steepest descent direction is proposed in this paper for a class of nonlinear programming problems. The solutions of the dynamic system, modelled with the conformable fractional derivative are investigated to obtain the minimizing point of the optimization problem. For this purpose, we use a step variational iteration method, adapted to use a conformable integral definition. Numerical simulations and comparisons show that the conformable fractional gradient based dynamic system is both feasible and efficient for a certain class of equality constrained optimization problems. Furthermore, the step variational iteration method, combined with the conformable integral definition, is a reliable tool for solving a system of fractional differential equations.
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The dynamics of multiparticle collisions in motion of a granular material

63%
Leszczyński J.
Open Physics
|
2003
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vol. 1
|
issue 4
596-605
EN
We consider the complex problem of how to calculate particle motions taking into account multiparticle collisions. Multiparticle contacts occur when a particle collides with neighbouring particles, so that those contacts have a direct influence on each other. We will focus on the molecular dynamics method. Particularly, we will analyse what happens in cohesive materials during multiparticle contacts. We investigated the expression of repulsive force formulated under fractional calculus which is able to control dynamically the transfer and dissipation of energy in granular media. Such approach allows to perform simulations of arbitrary multiparticle collisions and also granular cohesion dynamics.
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