scholarly journals Taming Hyperchaos with ESDDFD Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

2021 ◽  
Author(s):  
Gregory Gibson ◽  
Dominic Clemence-Mkhope
Keyword(s):  
Finite Difference ◽  
Fractional Derivative ◽  
Numerical Experiments ◽  
Financial System ◽  
Discrete Models ◽  
Conformable Fractional Derivative

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

scholarly journals Taming Hyperchaos with ESDDFD Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

2021 ◽  
Author(s):  
Gregory Gibson ◽  
Dominic Clemence-Mkhope
Keyword(s):  
Finite Difference ◽  
Fractional Derivative ◽  
Numerical Experiments ◽  
Financial System ◽  
Discrete Models ◽  
Conformable Fractional Derivative

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

scholarly journals Taming Hyperchaos with Exact Spectral Derivative Discretization Finite Difference Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

2022 ◽  
Vol 27 (1) ◽  
pp. 4
Author(s):  
Dominic P. Clemence-Mkhope ◽  
Gregory A. Gibson
Keyword(s):  
Finite Difference ◽  
Fractional Derivative ◽  
Numerical Experiments ◽  
Financial System ◽  
Discrete Models ◽  
Conformable Fractional Derivative ◽  
Finite Difference Discretization ◽  
Difference Discretization

Four discrete models, using the exact spectral derivative discretization finite difference (ESDDFD) method, are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is, in part, an artifact of the CEFD method, as it is absent from the ESDDFD models.

scholarly journals The Limited Validity of the Conformable Euler Finite Difference Method and an Alternate Definition of the Conformable Fractional Derivative to Justify Modification of the Method

2021 ◽  
Vol 26 (4) ◽  
pp. 66
Author(s):  
Dominic Clemence-Mkhope ◽  
Belinda Clemence-Mkhope
Keyword(s):  
Finite Difference ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Euler Method ◽  
Market Model ◽  
Alternative Methods ◽  
Conformable Fractional Derivative ◽  
Initial Value ◽  
Relaxation Equation ◽  
Definition Of

A method recently advanced as the conformable Euler method (CEM) for the finite difference discretization of fractional initial value problem Dtαyt = ft;yt, yt0 = y0, a≤t≤b, and used to describe hyperchaos in a financial market model, is shown to be valid only for α=1. The property of the conformable fractional derivative (CFD) used to show this limitation of the method is used, together with the integer definition of the derivative, to derive a modified conformable Euler method for the initial value problem considered. A method of constructing generalized derivatives from the solution of the non-integer relaxation equation is used to motivate an alternate definition of the CFD and justify alternative generalizations of the Euler method to the CFD. The conformable relaxation equation is used in numerical experiments to assess the performance of the CEM in comparison to that of the alternative methods.

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

scholarly journals Series method to solve conformable fractional ric-cati differential equations

2017 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Mohammed Al Masalmeh
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Control ◽  
Series Solution ◽  
Stochastic Games ◽  
Variable Coefficients ◽  
Conformable Fractional Derivative ◽  
Series Method ◽  
Previous Definition ◽  
Hyperbolic Boundary

This paper investigates and states some properties of conformable fractional derivative, Further Study and applies the series solution for a case of conformable fractional Riccati deferential equation with variable coefficients “which is arising in stochastic games” or “hyperbolic boundary control." Recently, Prof. Roshdi Khalil introduced a new and interesting definition for the C F D, which is simpler than the previous definition in Caputo and Riemann-Liouville. It leads to many extensions of the classical theorems in calculus.

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

Sign in / Sign up

Export Citation Format

Share Document