Is there any researcher working on a modeling different diseases using fractional operators?

There are many numerical techniques for obtaining approximate solutions of fractional order boundary value problems in which the order of differential equation is a fractional constant number. If we assume that the order of BVP is a continuous functions with respect to the time, then is there any numerical technique to obtain approximate solutions of a variable-order fractional BVP?

In fractional calculus many fractional operators, but their applications area unknown. Can you help me to determined the real Phenomena which we can apply the Capotu conformable fractional derivatives ?

Dear Researchers,

In recent years, two fractional derivatives are introduced by well-known mathematicians for modelling different phenomena. These operators are:

1. Caputo-Fabrizio fractional derivative,

2. Atangana-Baleanu fractional derivative.

The main difference of these newly-defined operators in comparison to the previous ones (The Caputo or Riemann-Liouville derivatives) is that their kernel is non-singular. This advantage absorbed the attention of many researchers to itself. Now, I have the following question:

Which fractional nonsingular derivative (the above operators) gives the more accurate results in modelling of real-world phenomena?

Thank you very much.

Best regards

Dear researchers

As you know, nowadays, most of the real-world phenomena are modeled by using different fractional operators. Among them, the Caputo and Riemann-Liouville fractional derivatives are the most famous for modeling the processes. Also, in the recent years, two other fractional derivatives called "Caputo-Fabrizio" and "Atangana-Baleanu" are used in many mathematical models. My main question in this regard is:

" What is the physical interpretation of the fractional derivation operators?"