  In this paper, a detrimental mathematical mistake is pointed out in the proof
of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the
gradient method with fractional order gradient direction, J. Franklin Inst.,
357 (2020) 2514-2532]}. It is highlighted that the way the authors prove the
convergence of the fractional extreme points of a real valued function to its
integer order extreme points lacks correct and valid mathematical argument.
Rest of the theorems contained in the paper are mostly announced without any
proof relaying on that of Theorem 1.
