  The least squares method provides the best-fit curve by minimizing the total
squares error. In this work, we provide the modified least squares method based
on the fractional orthogonal polynomials that belong to the space
$M_{n}^{\lambda} :=
\text{span}\{1,x^{\lambda},x^{2\lambda},\ldots,x^{n\lambda}\},~\lambda \in
(0,2]$. Numerical experiments demonstrate how to solve different problems using
the modified least squares method. Moreover, the results show the advantage of
the modified least squares method compared to the classical least squares
method. Furthermore, we discuss the various applications of the modified least
squares method in the fields like fractional differential/integral equations
and machine learning.
