Problem in plotting the system of fractional equations

Hello,

I'm facing a problem when drawing a system of fractional differential equations: the uninfected cells decrease to zero, while in a system of ordinary differential equations they increase and then stabilize. Why is this? And how can I solve this problem?

Thankyou

[John D'Errico]

It might be you have formulated it improperly, essentially solving a different problem than you think.

It might be you made a mistake in the code. Even many mistakes.

It might be there are instabilities you are not properly handling.

It might be ... lots of things, as I am sure I only touched the surface.

Can anyone know what you are doing "wrong"? Of course not, since you only gave a very vague description of that you are trying to solve, and you have said nothing at all about specifically what you did to try to solve the problem.

If you want help, then you need to make it possible for someone to help you. Show the code you wrote. Show the exact problem you tried to solve with that code. Explain the results which you think are incorrect, for that problem. Even better, show the plots you got, which seem to be wrong. Then you will have a chance of getting useful help.

Answer 1

[Sam Chak]

Hi @Amal Matrafi,

Have you considered using the Oustaloup recursive approximation to simulate fractional differential equations? The method converts a fractional‑order equation into an equivalent high‑order integer‑order system that can be solved with conventional numerical solvers.

If you wish to stabilize the fractional‑order system, Mittag–Leffler stability can serve as a basis for designing stable fractional‑order controllers.