Anomalous Relaxation in Dielectrics with Hilfer Fractional Derivative - Plata, A. R. G 'omez; Rosa, E. Capelas de Oliveira; Ester C. A. F. (Journal of Applied Nonlinear Dynamics, 2026)
We introduce a new relaxation function depending on an arbitrary parameter as a solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami regarding, anomalous relaxation in dielectrics, which are recovered as particular cases. We propose a differential equation introducing a fractional operator written in terms of the Hilfer fractional derivative of order ξ, with 0 < ξ ≤ 1 and type η, with 0 ≤ η ≤ 1. To discuss the solution of the fractional differential equation, the methodology of Laplace transform is required. As a by product we mention particular cases where the solution is completely monotone. %Some graphics show the behaviour of this completely monotone function. Finally, the empirical models are recovered as particular cases.