Problem Types
The general fractional differential equations problem type:
FractionalDiffEq.FDEProblem
— TypeFDEProblem
General type for all kinds of problems in FractionalDiffEq.jl.
FODE Problem
Fractional ordinary problems type, we can classified them as Single-Term and Multi-Term problems:
\[D^{\alpha}y(t)=f(t, y)\]
\[\sum_{s=0}^pc_sD^{\beta_s}y=f\]
FractionalDiffEq.SingleTermFODEProblem
— TypeSingleTermFODEProblem(f, α, u0, tspan)
Define a single term fractional ordinary differential equation, there are only one fractional differential operator in this problem.
FractionalDiffEq.MultiTermsFODEProblem
— TypeMultiTermsFODEProblem(parameters, orders, rightfun, u0, T)
MultiTermsFODEProblem(parameters, orders, rightfun, rparameters, rorders, u0, T)
Define a multi-terms fractional ordinary differential equation.
FractionalDiffEq.FODESystem
— TypeFODESystem(f, α, u0, tspan, p)
Define system of fractional differential equations.
FFODE Problem
FractionalDiffEq.FFPODEProblem
— TypeFFPODEProblem(f, α, u0, tspan, p)
Define fractal-fractional differential equations problems with power law kernel.
FractionalDiffEq.FFEODEProblem
— TypeFFEODEProblem(f, α, u0, tspan, p)
Define fractal-fractional differential equations problems with expoenntial decay kernel.
FractionalDiffEq.FFMODEProblem
— TypeFFMODEProblem(f, α, u0, tspan, p)
Define fractal-fractional differential equations problems with Mittag Leffler kernel.
FPDE Problem
Missing docstring for FractionalDiffEq.FPDEProblem
. Check Documenter's build log for details.
FDDE Problem
FractionalDiffEq.FDDEProblem
— TypeFDDEProblem(f, ϕ, α, τ, tspan)
Construct a fractional delayed differential equation problem.
FractionalDiffEq.FDDEMatrixProblem
— TypeFDDEMatrixProblem(α, τ, A, B, f, x0, tspan)
Construct a fractional matrix differential equation with delay with general form:
\[D_{t_0}^\alpha\textbf{x}(t)=\textbf{A}(t)\textbf{x}(t)+\textbf{B}(t)\textbf{x}(t-\tau)+\textbf{f}(t)\]
FractionalDiffEq.FDDESystem
— TypeFDDESystem(f, ϕ, α, τ, T)
Construct system of fractional delay differential equations problem.
DODE Problem
FractionalDiffEq.DODEProblem
— TypeDODEProblem(parameters, orders, interval, tspan, rightfun)
Define distributed order differential equation problem.
Fractional Difference Problem
FractionalDiffEq.FractionalDifferenceProblem
— TypeFractionalDifferenceProblem(f, α, x0)
Define fractional difference equation problems.
FractionalDiffEq.FractionalDifferenceSystem
— TypeFractionalDifferenceSystem(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 $x(i)$.
FIE Problem
Missing docstring for FractionalDiffEq.FIEProblem
. Check Documenter's build log for details.