Research Article Synchronization in Dynamically Coupled Fractional-Order Chaotic Systems: Studying the Effects of Fractional Derivatives J. L. Echenaus´ ıa-Monroy , 1 C. A. Rodr´ ıguez-Mart´ ıne , 1 L. J. Ontañ ´ on-Garc´ ıa , 2 J. Alvarez, 1 and J. Pena Ramirez 1 1 Applied Physics Division, Center for Scientific Research and Higher Education at Ensenada, CICESE. Carr. Ensenada-Tijuana, 3918 Zona Playitas, Ensenada, 22860 BC, Mexico 2 Coordinaci´ on Acad´ emica Regi´ on Altiplano Oeste, Universidad Aut´ onoma de San Luis Potos´ ı, Carretera a Santo Domingo 200, 78 600, Salinas de Hidalgo, S.L.P, Mexico CorrespondenceshouldbeaddressedtoJ.L.Echenaus´ ıa-Monroy;jose.luis.echenausia@gmail.comandJ.PenaRamirez; jpena@cicese.mx Received 27 August 2021; Revised 23 October 2021; Accepted 4 December 2021; Published 24 December 2021 Academic Editor: Atila Bueno Copyright © 2021 J. L. Echenaus´ ıa-Monroy et al. is is an open access article distributed under the Creative Commons AttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkis properly cited. is study presents the effectiveness of dynamic coupling as a synchronization strategy for fractional chaotic systems. Using an auxiliary system as a link between the oscillators, we investigate the onset of synchronization in the coupled systems and we analytically determine the regions where both systems achieve complete synchronization. In the analysis, the integration order is considered as a key parameter affecting the onset of full synchronization, considering the stability conditions for fractional systems. e local stability of the synchronous solution is studied using the linearized error dynamics. Moreover, some statistical metrics such as the average synchronization error and Pearson’s correlation are used to numerically identify the synchronous behavior. Two particular examples are considered, namely, the fractional-order R¨ ossler and Chua systems. By using bifurcation diagrams,itisalsoshownthattheintegrationorderhasastronginfluencenotonlyontheonsetoffullsynchronizationbutalsoon the individual dynamic behavior of the uncoupled systems. 1. Introduction Synchronization is an emergent physical phenomenon caused by the interaction of two or more dynamic entities that pervade the natural world [1–4]. In the case of oscil- lating units, the synchronization phenomenon can be de- fined as the adjustment of temporal evolution to a common rhythm. Forthecaseofinteger-ordersystems,thereexistsavastand mature literature where we can find different interconnection schemes for synchronizing dynamic systems, like, for example, master-slave synchronization scheme, adaptive synchroniza- tion, and synchronization based on state observers, to name a few [5–10]. Although each of these strategies is effective, there are limitations in their applications, e.g., there are cases where theseschemeshavemarginalrangesforwhichthesynchronous response is achieved or have poor robustness to maintain a stable synchronous state under the influence of external dis- turbances. is is one of the reasons why dynamic intercon- nections have emerged as an alternative to the classical static schemes. In this case, the interaction between agents is indi- rectly achieved through a suitably designed dynamic coupling [11–13].istypeofsynchronizationstrategyhasshownbetter performance than static couplings. In particular, dynamic coupling increases the intervals of coupling strength values for which it is possible to achieve synchronized behavior, and it may also be possible to synchronize systems that cannot be synchronized with static coupling [11]. Ontheotherhand,theuseoffractionalcalculushasbeen extensively studied in nonlinear systems (see, e.g., [14–18]) and also, there exist notable contributions related to the study of synchronization in fractional-order systems (see, Hindawi Complexity Volume 2021, Article ID 7242253, 12 pages https://doi.org/10.1155/2021/7242253