Problem Types

FDEProblem

General type for all kinds of problems in FractionalDiffEq.jl.

SingleTermFODEProblem(f, α, u0, tspan)

Define a single term fractional ordinary differential equation, there are only one fractional differential operator in this problem.

MultiTermsFODEProblem(parameters, orders, rightfun, u0, T)

MultiTermsFODEProblem(parameters, orders, rightfun, rparameters, rorders, u0, T)

Define a multi-terms fractional ordinary differential equation.

FODESystem(f, α, u0, tspan, p)

Define system of fractional differential equations.

FFPODEProblem(f, α, u0, tspan, p)

Define fractal-fractional differential equations problems with power law kernel.

FFEODEProblem(f, α, u0, tspan, p)

Define fractal-fractional differential equations problems with expoenntial decay kernel.

FFMODEProblem(f, α, u0, tspan, p)

Define fractal-fractional differential equations problems with Mittag Leffler kernel.

FDDEProblem(f, ϕ, α, τ, tspan)

Construct a fractional delayed differential equation problem.

FDDEMatrixProblem(α, τ, A, B, f, x0, tspan)

Construct a fractional matrix differential equation with delay with general form:

\[D_{t_0}^\alpha\textbf{x}(t)=\textbf{A}(t)\textbf{x}(t)+\textbf{B}(t)\textbf{x}(t-\tau)+\textbf{f}(t)\]

FDDESystem(f, ϕ, α, τ, T)

Construct system of fractional delay differential equations problem.

DODEProblem(parameters, orders, interval, tspan, rightfun)

Define distributed order differential equation problem.

FractionalDifferenceProblem(f, α, x0)

Define fractional difference equation problems.

FractionalDifferenceSystem(f, α, u0)

Define Fractional Difference System with the general constructure:

\[{^G\nabla_k^\alpha x(k+1)}=f(x(k))\]

With given initial condition $x(i)$.