Editing Fractional calculus (section)

===Riemann–Liouville fractional derivative===
The corresponding derivative is calculated using Lagrange's rule for differential operators. To find the {{mvar|α}}th order derivative, the {{mvar|n}}th order derivative of the integral of order {{math|(''n'' − ''α'')}} is computed, where {{mvar|n}} is the smallest integer greater than {{mvar|α}} (that is, {{math|''n'' {{=}} {{ceil|''α''}}}}). The Riemann–Liouville fractional derivative and integral has multiple applications such as in case of solutions to the equation in the case of multiple systems such as the tokamak systems, and Variable order fractional parameter.<ref name="Mostafanejad">{{Cite journal|doi = 10.1002/qua.26762|title = Fractional paradigms in quantum chemistry |year = 2021|last = Mostafanejad |first = Mohammad |journal = International Journal of Quantum Chemistry |volume = 121|issue = 20 |doi-access = free }}</ref><ref name="Al-Raeei">{{Cite journal|doi = 10.1016/j.chaos.2021.111209|title = Applying fractional quantum mechanics to systems with electrical screening effects |year = 2021|last = Al-Raeei|first = Marwan | url=https://www.sciencedirect.com/science/article/abs/pii/S0960077921005634 |journal = Chaos, Solitons & Fractals |volume = 150|issue = September|pages = 111209|bibcode = 2021CSF...15011209A }}</ref> Similar to the definitions for the Riemann–Liouville integral, the derivative has upper and lower variants.<ref>{{cite book |editor-last=Herrmann |editor-first=Richard |date=2014 |title=Fractional Calculus: An Introduction for Physicists |edition=2nd |location=New Jersey |publisher=World Scientific Publishing Co. |page=[https://books.google.com/books?id=60S7CgAAQBAJ&pg=PA54 54]{{Verify source |date=July 2020}}|isbn=978-981-4551-07-6|doi=10.1142/8934 |bibcode=2014fcip.book.....H}}</ref>
<math display="block">\begin{align}
  \sideset{_a}{_t^\alpha}D f(t) &= \frac{d^n}{dt^n} \sideset{_a}{_t^{-(n-\alpha)}}Df(t) \\
    &= \frac{d^n}{dt^n} \sideset{_a}{_t^{n-\alpha}}I f(t) \\
  \sideset{_t}{_b^\alpha}D f(t) &= \frac{d^n}{dt^n} \sideset{_t}{_b^{-(n-\alpha)}}Df(t) \\
    &= \frac{d^n}{dt^n} \sideset{_t}{_b^{n-\alpha}}I f(t)
\end{align}</math>