Fractional Differential Equation not supported

SciML / DifferentialEquations.jl

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

https://docs.sciml.ai/DiffEqDocs/stable/

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Fractional Differential Equation not supported #461

Open freemin7 opened 5 years ago

freemin7 commented 5 years ago

There is a class of differential equations which is not yet supported. It is still an area of active research and has little tooling or no in other Differential equation packages. Even if no FDE solver are going to be implemented in this package, looking at the (data and cache) structures needed to encode/run FDE efficiently might lead to new insights for "normal" DE solving. DOI: 10.3390/math6020016 seems to be an good introductory material.

ChrisRackauckas commented 5 years ago

Yup, I know we're missing this, and tooling for integro differential equations, and want to get something together for users.

freemin7 commented 5 years ago

Great, i took me longer than you answering to realize that Fractional Differential equation are a special case (and generalized case) of Integro-Differential equations. Great to hear that you are having that in mind. DifferentialEquations.jl really promises to be an objectively superior library.