Fractional conformable derivatives of Liouville-Caputo type with low-fractionality

This paper presents a novel fractional conformable derivative of Liouville-Caputo type of fractional order alpha = n - epsilon that contains a small epsilon and positive integer n values between [1;2]. The method is applied to obtain analytical solutions for the electrical circuits LC and RL and for the equations that describe the motion of a charged particle in an electromagnetic field using an expansion of the fractional conformable derivative in epsilon = n - alpha. Numerical simulations were obtained for different values of the fractional order and the parameter epsilon. This novel fractional conformable derivative allows describing physical systems where the level of fractality is low, such as oscillators, quantum dynamics, electromagnetic fields, mechanics of fractal and complex media, among others. (C) 2018 Elsevier B.V. All rights reserved.