Research Article Regression Coefficient Derivation via Fractional Calculus Framework Muath Awadalla , 1 Yves Yannick Yameni Noupoue , 2 Yucel Tandogdu , 3 and Kinda Abuasbeh 1 1 Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia 2 Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA), Universite Catholique de Louvain (UCLouvain), Louvain-la-Neuve 1348, Belgium 3 Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Via Mersin 10, Turkey Correspondence should be addressed to Muath Awadalla; mawadalla@kfu.edu.sa Received 8 January 2022; Revised 17 February 2022; Accepted 23 February 2022; Published 9 April 2022 Academic Editor: Melike Kaplan Copyright © 2022 Muath Awadalla et al. 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. is study focuses on deriving coefficients of a simple linear regression model and a quadratic regression model using fractional calculus. e work has proven that there is a smooth connection between fractional operators and classical operators. Moreover, it has also been shown that the least squares method is classically used to obtain coefficients of linear and quadratic models that are viewed as special cases of the more general fractional derivative approach which is proposed. 1.Introduction Initial concepts of fractional calculus (FC) can be traced back to seventeenth century when Isaac Newton, Leibniz, and L’ Hospital discussed preliminary ideas that shed light to future developments on FC. A considerable time elapsed before mathematicians returned to discuss the idea of FC. In 1819, Lacroix [1] mentioned the derivative of arbitrary order. Euler and Fourier also mentioned the derivatives of an arbitrary order. e first applications are made by Abel [2] in 1823. Ross [3] provided a historical track on the funda- mental theory of FC. e new research trend in FC since last century focuses on the investigation of its application in real life problems. In this regard, researchers have produced thousands of articles from various branches of sciences in which they showed how some problems defined in the classical calculus could be converted into FC problems. Another class of researchers in the fields consists of those who not only defined fractional calculus approach of solving problems but who also man- aged to show in their works that the FC might be more efficient than its classical counterpart in solving problems. In either case, it is common for researchers to back up their FC finding with similar results from classical calculus. Fractional differential equations are a part of FC in which a substantial amount of work has been undertaken aiming to prove the power of the method over the classical differential equations. Works carried out along these lines with appli- cations in Biology [4, 5], Physics [6], and Finance [7] are just a few to mention. Some more recent work on FC worth to mention are found, for instance, in [8], where the authors investigated bending of the beam using fractional differential equations. Sumelka et al. [9] reformulated the classical Euler–Bernoulli beam theory using fractional calculus. Stempin and Sumelka [10] studied the bending analysis of nanobeams aiming to improve the space-fractional Euler–Bernoulli beam (s-FEBB) theory. Sidhardh et al. [11]. presented their findings on their studies of the analytical and finite element formulation of a geometrically nonlinear and fractional-order nonlocal model of a Euler–Bernoulli beam. e size-dependent bending behavior of nanobeams is studied by Oskouie et al. [12] employing the Euler–Bernoulli beam theory, where the nonlocal effects are obtained via fractional calculus. Hindawi Journal of Mathematics Volume 2022, Article ID 1144296, 9 pages https://doi.org/10.1155/2022/1144296