The Gradient descent method from the perspective of fractional calculus

Motivated by gradient methods in optimization theory, we give methods based on psi-fractional derivatives of order α in order to solve unconstrained optimization problems. The convergence of these methods is analyzed in detail. This paper also presents an Adams-Bashforth-Moulton (ABM) method for the estimation of solutions to equations involving psi-fractional derivatives. Numerical examples using the ABM method show that the fractional order α and weight psi are tunable parameters, which can be helpful for improving the performance of gradient descent methods.