Problem Types

The general fractional differential equations problem type:

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.SingleTermFODEProblemType
SingleTermFODEProblem(f, α, u0, tspan)

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

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FractionalDiffEq.MultiTermsFODEProblemType
MultiTermsFODEProblem(parameters, orders, rightfun, u0, T)

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

Define a multi-terms fractional ordinary differential equation.

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FFODE Problem

FPDE Problem

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FDDE Problem

FractionalDiffEq.FDDEProblemType
FDDEProblem(f, ϕ, α, τ, tspan)
  • f: The function describing fractional delay differential equations.
  • ϕ: History function

Construct a fractional delayed differential equation problem.

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FractionalDiffEq.FDDEMatrixProblemType
FDDEMatrixProblem(α, τ, A, B, f, x0, tspan)

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

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

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DODE Problem

Fractional Difference Problem

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FIE Problem

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Missing docstring for FractionalDiffEq.FIEProblem. Check Documenter's build log for details.