Research Article AnalysisofaFour-DimensionalHyperchaoticSystemDescribedby the Caputo–Liouville Fractional Derivative Ndolane Sene Laboratoire Lmdan, D´ epartement de Math´ ematiques de la D´ ecision, Universit´ e Cheikh Anta Diop de Dakar, Facult´e des Sciences Economiques et Gestion, BP 5683 Dakar Fann, Senegal CorrespondenceshouldbeaddressedtoNdolaneSene;ndolanesene@yahoo.fr Received 5 September 2020; Revised 13 October 2020; Accepted 18 November 2020; Published 28 November 2020 AcademicEditor:MustafaCagriKutlu Copyright © 2020 Ndolane Sene. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Anewfour-dimensionalhyperchaoticfinancialmodelisintroduced.enoveltiescomefromthefractional-orderderivativeand theuseofthequadricfunction x 4 inmodelingaccuratelythefinancialmarket.eexistenceanduniquenessofitssolutionshave beeninvestigatedtojustifythephysicaladequacyofthemodelandthenumericalschemeproposedintheresolution.Weoffera numerical scheme of the new four-dimensional fractional hyperchaotic financial model. We have used the Caputo–Liouville fractionalderivative.eproblemsaddressedinthispaperhavemuchimportancetoapproachtheinterestrate,theinvestment demand,thepriceexponent,andtheaverageprofitmargin.evalidationofthechaotic,hyperchaotic,andperiodicbehaviorsof theproposedmodel,thebifurcationdiagrams,theLyapunovexponents,andthestabilityanalysishasbeenanalyzedindetail.e proposednumericalschemeforthehyperchaoticfinancialmodelisdestinedtohelptheagentsdecideinthefinancialmarket.e solutions of the 4D fractional hyperchaotic financial model have been analyzed, interpreted theoretically, and represented graphicallyindifferentcontexts.epresentpaperismathematicalmodelingandisanewtoolineconomicsandfinance.Wealso confirm, as announced in the literature, there exist hyperchaotic systems in the fractional context, which admit one positive Lyapunov exponent. 1. Introduction Manybehaviorsofthedynamicalsystemsaredeterministic. e systems’ future behaviors follow the same evolutions andareexplainedbytheinitialconditionsandthepastofthe systems. Chaos theory is one of the mathematical domain which studies these types of dynamical systems and has received many investigations [1, 2]. Lorenz [2] was the first author to propose the chaotic system in three-dimensional space,namely,chaoticattractor.Lorenz’sworkcanprobably be considered as the beginning of this discipline. It is well knownthechaoticsystemsarenonlineardynamicalsystems andaresensitivetotheirinitialconditions.atis,whenthe initial conditions of the considered system have small dif- ferences or changes, it becomes complicated to predict the behaviors of the system [1]. is field of mathematics is strongly in relation to the control theory. is reason ex- plains the many investigations related to chaos control. In general,thecontrollerstrytoeliminatethechaoticbehaviors using synchronization methods or other techniques. Many studies also focus on the stability analysis of the chaotic systems[1,3].Chaoticbehaviorsareobservedinmanyreal- worldproblems,influidflows,inweatherandclimate[2],in the stock market, in road traffics, and others. Chaos theory has many applications, too, in anthropology, computer science,economic[1],biology,physics[1],meteorology,and others. After Lorenz’s proposition, many other types of chaotic systems appear in the literature. Recent investiga- tions focus on the chaotic and hyperchaotic systems in economics;wehavethechaoticfinancialsystemwiththree- dimensional space (see in [4, 5]); we have the four-di- mensional hyperchaotic financial model. Chaotic and hyperchaotic systems have many applica- tionsinfinanceandeconomics.ereexistmanynonlinear dynamical systems in finance markets that use chaotic systems to predict the markets’ behavior. In [1], Xin et al. Hindawi Complexity Volume 2020, Article ID 8889831, 20 pages https://doi.org/10.1155/2020/8889831