Research Article On the Controllability of Conformable Fractional Deterministic Control Systems in Finite Dimensional Spaces Maher Jneid 1 and Muath Awadalla 2 1 Departement of Mathematics and Computer Science, Faculty of Science, eirut Arab University, eirut, Lebanon 2 Departement of Mathematics and Statistics, King Faisal University, Al-Ahsaa, Hufuf, Saudi Arabia Correspondence should be addressed to Maher Jneid; m.jneid@bau.edu.lb Received 7 October 2019; Accepted 23 December 2019; Published 10 March 2020 Academic Editor: Attila Gil´ anyi Copyright © 2020 Maher Jneid and Muath Awadalla. is is an open access article distributed under the Creative Commons AttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkis properly cited. In this paper, we establish a set of convenient conditions of controllability for semilinear fractional finite dimensional control systemsinvolvingconformablefractionalderivative.Indeed,sufficientconditionsofcontrollabilityforasemilinearconformable fractionalsystemarepresented,assumingthatthecorrespondinglinearsystemsarecontrollable.epresentmethodisbasedon conformablefractionalexponentialmatrix,Gramianmatrix,andtheiterativetechnique.Twoillustratedexamplesarecarriedout to establish the facility and efficiency of this technique. 1.Introduction Controllability concepts have played a substantial role in several fields in engineering, control theory, and applied mathematics.In1960,thecontrollabilitywasfirstdefinedby Kalman [1] as a property of shifting the systems from any initialstatevalueintoanystatevalueataterminaltime.is definition was divided into two notions: an exact and an approximatecontrollabilitywhichbecomemoresuitablefor dealing with control systems in infinite dimensional spaces. e purpose of those notions is the existence of control systems which are approximately controllable, but are not exact (see [2]). In fact, the term exact controllability would refer to as a controllability which is the same as defined by Kalman. However, the definition of approximate control- lability is determined by transferring the systems from any initial state value into some small neighbourhood of any point at terminal time in the state space. Later on, many researchers conducted pioneering studies in an attempt to obtain proper controllability conditions (exact and ap- proximate)forthelinearandnonlinearcontrolsystems(see, for example, [3–8] and the references cited therein). Manyproblemsintherealworldcanbemodelledpurely byfractionaldifferentialequations(formoredetails,referto [9, 10]). is new calculus has pointedly attracted the mathematicians to focus clearly on revealing better results. e concept of controllability was extended to fractional control systems by various investigators. For instance, Sakthiveletal.[11]utilizedfixedpointapproachtoprovethe controllability of nonlinear fractional systems. Vijayakumar et al. [12] obtained the controllability conditions for frac- tional integrodifferential neutral control systems with nonlocal conditions. Ma and Liu [13] employed analytic methodsandresolventoperatortoinvestigatecontrollability conditions and continuous dependence of a fractional neutral integrodifferential equation involving state-depen- dent delay. Jneid [14] derived sufficient conditions of ap- proximate controllability for semilinear integrodifferential systems of fractional order with nonlocal conditions by using compact semigroup operator and Schauder fixed- point theorem. Sakthivel et al. [15] studied the approximate controllability conditions for nonlinear fractional stochastic differential inclusions, providing that the corresponding linearpartisapproximatelycontrollable.Chokkalingamand Baleanu [16] obtained a set of sufficient conditions for controllability for fractional functional integrodifferential systems involving the Caputo fractional derivative of order α ∈ (0, 1] in Banach spaces. Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2020, Article ID 9026973, 7 pages https://doi.org/10.1155/2020/9026973