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Motivated by gradient methods in optimization theory, we give methods basedon $\psi$-fractional derivatives of order $\alpha$ in order to solveunconstrained optimization problems. The convergence of these methods isanalyzed in detail. This paper also presents an Adams-Bashforth-Moulton (ABM)method for the estimation of solutions to equations involving $\psi$-fractionalderivatives. Numerical examples using the ABM method show that the fractionalorder $\alpha$ and weight $\psi$ are tunable parameters, which can be helpfulfor improving the performance of gradient descent methods.

The Gradient descent method from the perspective of fractional calculus