## 1 Introduction
The fractional derivative with exponential and non-singular kernel defined by [PERSON] and [PERSON] is largely used in the modeling of dissipative phenomena by fractional derivatives. The Caputo-Fabrizio integral operator with exponential memory (so called fractional derivative with a non-singular kernel) is oriented to more complex relaxation processes than the ones modeled by the classical fractional derivatives with power-law (fractional derivatives with singular kernel) memories. Applications of the Caputo-Fabrizio integral operator with memory in the modeling of the dissipative phenomena with exponentially decaying relaxation functions have been discussed by [PERSON] [28]. It is known that the most popular function fitting the time-domain relaxation patterns is the Kohlraush stretched-exponential function [29]\(\varphi(k,t)=\exp(-(at)^{\alpha_{k}})\) where \(\alpha_{k}\), \(0\leq\alpha_{k}\leq 1\) is the stretching exponent and \(a\) is an inverse of the characteristic material time constant. [PERSON] et al. [30] showed that the Kohlraush relaxation function is a kernel derived from experiments. It is easy to notice that the Caputo-Fabrizio derivative operator has been constructed with a simple exponential memory; namely, the Kohlraush stretched exponent is set to one. In a similar way, a generalization of the Caputo-Fabrizio derivative was constructed by considering a kernel that generalizes the exponential function, namely the Mittag-Leffler function with a single parameter. The new operator is called the Atangana-Baleanu fractional derivative. The choosing of the memory kernel and the recovery of the relaxation function from the experimental data and fitting it with a well-defined function is a task strongly dependent on the physics of the process of interest. The memory kernels in the fractional differential operators used to model linear viscoelasticity correspond to the responses of the material,namely to the relaxation moduli and compliances [28]. It is important to note that Mittag-Leffler functions are solutions of some fractional differential equations; therefore, they are non-local functions. In consequence, the time-fractional Atangana-Baleanu derivative is a fractional derivative with non-singular and non-local kernel. It is expected that the non-locality of the Mittag-Leffler kernel allows better description of the memory within the structure and media with different scales. Also, it is known that Mittag-Leffler functions are suitable for interesting generalizations. Thus, generalizations of these functions with three or four parameters were studied. Considered to be the kernel of fractional derivatives, these functions become useful in describing some complex physical processes. For example, the three-parameter Mittag-Leffler functions studied by the Indian mathematician [PERSON] play an important role in describing anomalous dielectric relaxation, stochastic processes, or renewal processes [31]. [PERSON] et al. [32] studied four fractional viscoelastic models, namely the fractional Maxwell model, fractional Kelvin-Voigt model, fractional Zener model and fractional Poynting-Thomson model using the Riemann-Liouville and Caputo derivatives, as well as the Caputo-Fabrizio and Atangana-Baleanu derivatives. For each fractional viscoelastic model, the stress relaxation modulus, creep compliance and dynamic modulus have been derived and compared. Their results show that the fractional Maxwell model and fractional Zener model with the Mittag-Leffler function kernel do not provide accurate descriptions of the stress relaxation modulus at the shortest time and the storage modulus at the highest frequency. However, these results are not a verdict against the derivatives with non-singular and non-local kernel that could describe different complex processes.