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