Tracking the Trajectory of a Fractional Dynamical System When Measuring Part of State Vector Coordinates

2020 ◽  
Vol 56 (11) ◽  
pp. 1463-1471
Author(s):  
P. G. Surkov
Keyword(s):  
Dynamical System ◽  
State Vector ◽  
Fractional Dynamical System

Fractal–fractional dynamical system of Typhoid disease including protection from infection

2021 ◽  
Author(s):  
Qu Haidong ◽  
Mati ur Rahman ◽  
Muhammad Arfan ◽  
Mehdi Salimi ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Dynamical System ◽  
Fractional Dynamical System

scholarly journals On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 689 ◽  
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty ◽  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Coupled System ◽  
Dynamical Model ◽  
Transform Method ◽  
System Parameters ◽  
Nonlinear Coupled System ◽  
Differential Transform ◽  
Fractional Dynamical System

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.

Fractional Constrained Systems and Caputo Derivatives

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principles ◽  
Constrained Systems ◽  
Control Problems ◽  
Fractional Dynamics ◽  
Constrained System ◽  
Caputo Derivatives ◽  
Fractional Dynamical System ◽  
Made In

During the last few years, remarkable developments have been made in the theory of the fractional variational principles and their applications to control problems and fractional quantization issue. The variational principles have been used in physics to construct the phase space of a fractional dynamical system. Based on the Caputo derivatives, the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase space is discussed. Two examples of discrete constrained system are analyzed in detail.

Center Manifold of Fractional Dynamical System

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Li Ma ◽  
Changpin Li
Keyword(s):  
Dynamical System ◽  
Center Manifold ◽  
High Dimensional ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
Reduction Methods ◽  
Fractional Dynamical System ◽  
Lower Dimensional

Dimension reduction of dynamical system is a significant issue for technical applications, as regards both finite dimensional system and infinite dimensional systems emerging from either science or engineering. Center manifold method is one of the main reduction methods for ordinary differential systems (ODSs). Does there exists a similar method for fractional ODSs (FODSs)? In other words, does there exists a method for reducing the high-dimensional FODS into a lower-dimensional FODS? In this study, we establish a local fractional center manifold for a finite dimensional FODS. Several examples are given to illustrate the theoretical analysis.

Controllability criteria of fractional differential dynamical systems with non-instantaneous impulses

2019 ◽  
Vol 37 (3) ◽  
pp. 777-793
Author(s):  
B Sundara Vadivoo ◽  
R Raja ◽  
Jinde Cao ◽  
G Rajchakit ◽  
Aly R Seadawy
Keyword(s):  
Dynamical System ◽  
Algebraic Approach ◽  
Main Section ◽  
Volterra Type ◽  
Differential Systems ◽  
Gramian Matrix ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Fractional Dynamical System ◽  
Sufficiency Conditions

Abstract This manuscript prospects the controllability criteria of non-instantaneous impulsive Volterra type fractional differential systems. By enroling an appropriate Gramian matrix that is often defined by the Mittag-Leffler function and with the assistance of Laplace transform, the necessary and sufficiency conditions for the controllability of non-instantaneous impulsive Volterra-type fractional differential equations are derived by using algebraic approach and Cayley–Hamilton theorem. An important feature present in our paper is that we have taken non-instantaneous impulses into the fractional order dynamical system and studied the controllability analysis, since this do not exist in the available source of literature. Inclusively, we have provided two illustrative examples with the existence of non-instantaneous impulse into the fractional dynamical system. So this demonstrates the validity and efficacy of our obtained criteria of the main section.

Multistage Adomian Decomposition Method for Solving NLP Problems Over a Nonlinear Fractional Dynamical System

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Decomposition Method ◽  
Optimization Problem ◽  
Adomian Decomposition Method ◽  
Optimal Solution ◽  
Initial Time ◽  
Adomian Decomposition ◽  
Fractional Differential ◽  
Fractional Dynamical System

This paper deals with implementation of the multistage Adomian decomposition method (MADM) to solve a class of nonlinear programming (NLP) problems, which are reformulated with a nonlinear system of fractional differential equations. The multistage strategy is used to investigate the relation between an equilibrium point of the fractional order dynamical system and an optimal solution of the NLP problem. The preference of the method lies in the fact that the multistage strategy gives this relation in an arbitrary longtime interval, while the Adomian decomposition method (ADM) gives the optimal solution just only in the neighborhood of the initial time. The numerical results taken by the fractional order MADM show that these results are compatible with the solution of NLP problem rather than the ADM. Furthermore, in some cases the fractional order MADM can perform more rapid convergency to the optimal solution of optimization problem than the integer order ones.

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