# API

*Let's solve some differential equations!*

## Package features

- Solve fractional calculus problems

## Function Documentation

`FdeSolver.FDEsolver`

— Method`FDEsolver(F::Function, tSpan::Vector{<:Real}, y0::Union{Real, Vector{<:Real}, Matrix{<:Real}}, β::Union{Real, Vector{<:Real}}, par...; h = 2^-6, nc = 2, JF = nothing, tol = 1e-6, itmax = 100)`

Solves fractional differential equations with a predictor-corrector approach.

**Arguments**

`F::Function`

: the right side of the system of differential equations. It must be expressed in the form of a function and return a vector function with the same number of entries of order of derivatives. This function can also include a vector of parameters:`par...`

.`tSpan::Vector{<:Real}`

: the time span along which computation is performed.`y0::Union{Real, Vector{<:Real}, Matrix{<:Real}}`

: the initial values in the form of a row vector (`Vector{<:Real}`

) for $β <= 1$ and a matrix (`Matrix{<:Real}`

) for $β > 1$, where each column corresponds to the initial values of one differential equation and each row to the order of derivation.`β::Union{Real, Vector{<:Real}}`

: the orders of derivation in the form of a row vector, where each element corresponds to the order of one differential equation. It can take decimal as well as integer values.`JF::Function`

: the Jacobian of F. If not provided, the solver will evaluate the solution without the aid of the Jacobian matrix.`par...`

: additional parameters for the function F.`h::Real`

: the step size of the computation.`nc::Int64`

: the desired number of corrections for predictor-corrector method, when there is no Jacobian.`tol::Float64`

: the tolerance of errors, the norm inf of each iteration (for NR method) or correction when nc>10 (for PC method).`ìtmax::Int64`

: the maximal number of iterations.

To access the manual of `FDEsolver`

from the Julia REPL, type:

`?FDESolver`