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This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solution to this fractional model. Hence several numerical approaches, such as generalized Euler's method (GEM), power series expansion (PSE) method, and Caputo-Fabrizio (CF) method, were used to compute the solution. The classical solution obtained from the first order non-linear differential equation was also considered to enable the comparison of error levels.

This study focuses on deriving coefficients of a simple linear regression model and a quadratic regression model using fractional calculus. The 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.