As far as I'm concerned, the Caputo-Fabrizio derivative gives more accurate results. Because its kernel is exponential function.

Hi Sina Etemad

In the herb dynamical system, the classical time-derivative is modeled with the Atangana-Baleanu fractional-order operator which combines both nonlocal and nonsingular kernels in its formulation:

Article Analysis and simulation of herd behaviour dynamics based on ...

Comparative graphical analysis of the Atangana-Baleanu derivative for temperature, concentration, and velocity field, with slip and non-slip impact, shows that the memory effects of the Atangana-Baleanu derivative are better than the results that exist in the literature:

Article Computational Results With Non-singular and Non-local Kernel...

In another study, via the root sum squared approach, the efficiency rate of the fractional-order versions is found to be about 20%, 22.5%, and 24.7% for the Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo operators, respectively, for this particular MSEIR model:

Article Fractional derivatives applied to MSEIR problems: Comparativ...

Hope this helps!

Best regards,

Ebrahim

Caputo-Fabrizio: Mostly used when it comes to initial value problems.

Grunwald-Letnikov: Mostly used to get better results when it comes to numerical analysis.

Riemann–Liouville: Mostly used when it comes to continuous dynamical systems.

اعتذر لا امتلك اجابة دقيقة

https://www.researchgate.net/topic/Modeling

https://www.sciencedirect.com/science/article/pii/S2211379721001157

When it comes to an infectious disease, compartment model is very useful and accurate

سثث

https://clarivate.com/blog/fractional-derivative-modeling-real-world-problems/

As my best knowledge, the Caputo-Fabrizio derivative gives more accurate results

when you dealing with time, the best one is Caputo-fractional derivative

when you deal with the space, The best one is the Riesz-Feller operator

The answer is if the kernel of a given operator corresponds to the relaxation function of the modeled process. Then, it can be used as kernel, single kernels, or a series of kernels (thus leading to a series of fractional differential operators).

Some people believe that changing the operator, that can in a blind manner fit better experimental data.

Using the replacement technology in creating fractional-order models, actually, no-realistic models are created, but surrogate models (look for literature on surrogate modeling). Since there is an additional parameter, that is the fractional-order (commonly denoted as "alpha", appearing in the final solution, then changing it, one can obtain a variety of solutions of the surrogate solutions. For some "alpha" the surrogate solution may match experimental data, for others not, but matching does not mean that we have a solution corresponding to the physics, since the very beginning, when the replacement was done, the surrogate model disappeared from the physics and the rules of modeling are violated.

Thus, which kernel is better, is an unphysical question. Modeling, especially fractional-order modeling needs deep knowledge of the physics of dissipative processes, not only replacement and calculations with results that cannot be interpreted.

Some articles supporting my words are attached

Dear Prof. Jordan Hristov

Thanks a lot for your complete reply.

You already applied these

I have used Caputo for time and Feller-Riesz for space successfully in 22 highly impacted papers

I think that the kind of operator should be determined according to the specific dynamic process.

Good and correct answer Changlong Yu

I agree with Prof. Yu. In addition, the classical Caputo fractional derivative seems to be the best one in electronic engineering.

The answer lies within the question that how fractional derivatives give accurate results for modelling different phenomena.

All other fractional derivates, whatsoever the names, are derived from approximations of R-L derivative. Even Caputo is a special

case of R-L. So, researchers should answer how R-L derivative give more accurate results than the classical integer-order. The scientific

community (including me) is still trying to understand this.

Both the kernels are non-singular, so basically kernels are the control convergence parameters, if kernel are singular then we cant attain a good convergence. In this case the kernel of CF fractional derivative is constant and is different from the AB fractional derivative. So actually the AB kernel describe the complexity in very easy way and comprehensively.

We are so glad to hear about your achievement. You have always been an extraordinary one among us. Our best wishes are always with you and colleagues

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