Solve Fractional Differential Equation with FractionalDiffEq.jl | Qu | JuliaCon 2024

Fractional-order differential equations have increasingly gained attention as a compelling subject, particularly in recent decades, offering more nuanced representations in natural models from a fractional-order perspective. Tracing back to the origins of 'non-integer' calculus, a concept first contemplated by Leibniz and L'Hôpital, numerous scientific luminaries have contributed tirelessly to the advancement of fractional calculus. This field has proven particularly instrumental in accurately describing phenomena in diverse areas such as viscoelasticity, acoustics, rheology, and polymeric chemistry. Additionally, the application of fractional derivatives has emerged as an exceptionally fitting approach for characterizing the memory and hereditary properties inherent in a variety of materials and processes.

```julia
prob = FDEProblem(fun, order, u0, tspan)
sol = solve(prob, alg(), dt)
```

```julia
prob = FDDEProblem(fun, phi, order, u0, constant_lags=[tau], tspan)
sol = solve(prob, alg(), dt)
```

* Keep adding more high performance algorithms.
* Make the usage of API more simple and elegant.
* Write more illustrative documents for usability.
* Integrate with the SciML ecosystem to provide users more useful features.