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SciFracX / FractionalDiffEq.jl

Solve Fractional Differential Equations using high performance numerical methods
https://scifracx.github.io/FractionalDiffEq.jl/dev/
MIT License
80 stars 11 forks source link

Integrate w/ SciML? #2

Open azev77 opened 2 years ago

azev77 commented 2 years ago

Hi and thanks for this package! Looks really useful. Will this eventually work w/ @ChrisRackauckas's DifferentialEquations.jl?

ErikQQY commented 2 years ago

Hello there!😄 As you can see, this package is just started and algorithms or ecosystems are not so well. To be honest, I am a big fan of what Chris has done in DifferentialEquation.jl, and I am trying to follow the design pattern of OrdinaryDiffEq.jl. I think the integration would be very interesting and it would be very useful for users.

ChrisRackauckas commented 2 years ago

We'll reconnect later. We don't have a good interface for this right now. Though in the near future we will be able to specify Fractional PDEs with MTK, mainly for solving with NeuralPDE.jl, and it would be nice to connect over to this library. There could be a lot of nice connections as well, specifically https://github.com/SciFracX/FractionalCalculus.jl would be nice to use in NeuralPDE for the semi-discretization loss in the fractional derivatives. Thanks for pointing me here and I assume it will grow nicely.

ErikQQY commented 2 years ago

Looking forward to connecting! Ping me anytime if there are questions about this library :)

azev77 commented 2 years ago

Btw, I wrote a note about A General Theory of Fractional Operations. image It would be great if, eventually, all relevant operations could be generalized to allow for their fractional counterparts...

ErikQQY commented 2 years ago

@azev77 Sounds very interesting! Fractional multiplication, fractional difference, btw I know the fractional difference equations are also being used widely.🤔