# API

Let's solve some differential equations!

## Package features

• Solve fractional calculus problems

## Function Documentation

FdeSolver.FDEsolverMethod
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