Mathematical Modeling of Consolidation Dynamics on the Basis of Fractional-Differential Approach

2014 ◽  
Vol 46 (10) ◽  
pp. 1-10
Author(s):  
Vladimir M. Bulavatskiy ◽  
Yuriy G. Kryvonos
Keyword(s):  
Mathematical Modeling ◽  
Differential Approach ◽  
Fractional Differential

Simulation of Nonlinear Pyroelectric Response of Ferroelectrics near Phase Transition: Fractional Differential Approach

2020 ◽  
Vol 992 ◽  
pp. 843-848
Author(s):  
L. Moroz ◽  
Anna Maslovskaya
Keyword(s):  
Pyroelectric Coefficient ◽  
Ferroelectric Crystal ◽  
One Dimensional ◽  
Differential Approach ◽  
Thermal Distribution ◽  
Pyroelectric Current ◽  
Fractional Differential ◽  
Ferroelectric Single Crystal ◽  
Simulation Results ◽  
Pyroelectric Response

The paper is devoted to mathematical modeling pyroelectric current of ferroelectric single crystal under the conditions of intensive light heating in view of fractal behavior of these materials. The proposed approach is based on numerical simulation of thermal distribution in a ferroelectric sample using time fractional operator as well as computation of pyroelectric response. The simulation results for typical TGS ferroelectric crystal were described in one-dimensional case of the model in comparison with experimental data. Pyroelectric signals depending on temperature pyroelectric coefficient and thermal physical characteristics were also analyzed.

scholarly journals Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

2018 ◽  
Vol 11 (08) ◽  
pp. 994-1014 ◽  
Author(s):  
V. F. Morales-Delgado ◽  
J. F. Gómez-Aguilar ◽  
M. A. Taneco-Hernández ◽  
R. F. Escobar-Jiménez ◽  
V. H. Olivares-Peregrino
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Mathematical Modeling and Functional Order Pursuits with Separated Dynamics

2021 ◽  
Vol 2068 (1) ◽  
pp. 012002
Author(s):  
Mashrabjon Mamatov ◽  
Xakimjon Alimov
Keyword(s):  
Mathematical Modeling ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Order Equation ◽  
Matrix Functions ◽  
Pursuit Problem ◽  
Controlled Systems ◽  
Generalized Matrix ◽  
Fractional Differential ◽  
Qualitative Dynamics

Abstract This work is devoted to the study of the pursuit problem in controlled systems described by a fractional-order equation with divided dynamics. For fixed player controls, representations of solutions are established in the form of analogs of the Cauchy formula using generalized matrix functions. Sufficient conditions are obtained for the possibility of completing the pursuit. Specific types of fractional differential equations and models of fractional dynamical systems are considered. The qualitative dynamics, issues of stability and controllability of such systems are discussed. Considered, try which, the motion of the equation is described with irrational orders. Problems of the type under study are encountered in modeling the processes of economic growth and in problems of stabilizing dynamic systems.

scholarly journals FEATURES OF THE FRACTIONAL-DIFFERENTIAL APPROACH IMPLEMENTATION TO DESCRIBE THE PROCESS OF FEEDING A TWO-PHASE ZONE DURING SOLIDIFICATION OF METALS AND ALLOYS

2021 ◽  
pp. 88-91
Author(s):  
Tatjana Selivyorstova ◽  
Vadim Selivyorstov ◽  
Yuliia Mala
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Nonlinear Equation ◽  
Mathematical Models ◽  
Single Phase ◽  
Phase Zone ◽  
Two Phase ◽  
Diffusion Type ◽  
Differential Approach ◽  
Fractional Differential

To describe filtration processes in complex dendritic-porous media, a number of fractional-differential mathematical models of diffusion type have been proposed.A nonlinear equation containing fractional Riemann-Liouville derivatives with respect to time is described, which can be used to correctly describe the single-phase filtration of a non-Newtonian fluid in a porous medium.

scholarly journals A Novel FastSLAM Framework Based on 2D Lidar for Autonomous Mobile Robot

Electronics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 695
Author(s):  
Xu Lei ◽  
Bin Feng ◽  
Guiping Wang ◽  
Weiyu Liu ◽  
Yalin Yang
Keyword(s):  
Genetic Algorithm ◽  
Autonomous Navigation ◽  
Field Experiments ◽  
Autonomous Mobile Robot ◽  
Maximum Weight ◽  
Virtual Particle ◽  
Differential Approach ◽  
Weight Value ◽  
Environment Exploration ◽  
Fractional Differential

The autonomous navigation and environment exploration of mobile robots are carried out on the premise of the ability of environment sensing. Simultaneous localisation and mapping (SLAM) is the key algorithm in perceiving and mapping an environment in real time. FastSLAM has played an increasingly significant role in the SLAM problem. In order to enhance the performance of FastSLAM, a novel framework called IFastSLAM is proposed, based on particle swarm optimisation (PSO). In this framework, an adaptive resampling strategy is proposed that uses the genetic algorithm to increase the diversity of particles, and the principles of fractional differential theory and chaotic optimisation are combined into the algorithm to improve the conventional PSO approach. We observe that the fractional differential approach speeds up the iteration of the algorithm and chaotic optimisation prevents premature convergence. A new idea of a virtual particle is put forward as the global optimisation target for the improved PSO scheme. This approach is more accurate in terms of determining the optimisation target based on the geometric position of the particle, compared to an approach based on the maximum weight value of the particle. The proposed IFastSLAM method is compared with conventional FastSLAM, PSO-FastSLAM, and an adaptive generic FastSLAM algorithm (AGA-FastSLAM). The superiority of IFastSLAM is verified by simulations, experiments with a real-world dataset, and field experiments.

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