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  "body": "\n## Summary\n\nA fractional differential equation is a [[differential equation|003R0V5M7V]] in which derivatives of non-integer order of the unknown function appear.\nThese derivatives come from [[fractional calculus|T73XK15SA2]], most often the Riemann–Liouville or the [[Caputo derivative|6VMGQYF8RW]].\nBecause a fractional derivative is an integral over the whole past, such equations model processes with memory, such as viscoelastic materials and anomalous diffusion.\n\n## Explanations\n\n### L1 human\n\nAn ordinary derivative only looks at the function near one point.\nA fractional derivative, such as a derivative of order $1/2$, is a weighted average over all earlier times.\nSo the rate of change in a fractional equation depends on the whole history of the solution.\nFor example, the equation $D^{1/2} y = 1$ with $y(0) = 0$, with the Caputo derivative, has the solution $y(t) = 2\\sqrt{t/\\pi}$, the half integral of the constant $1$.\n",
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