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What is fractional calculus?

  1. Sep 12, 2010 #1
    the title says everything. I encountered this term and I wanted to know what fractional calculus is and what it does.
     
  2. jcsd
  3. Sep 12, 2010 #2

    MathematicalPhysicist

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    From the very little I read (and of which I can rememebr reading) from a textbook by Jerome Spanier and Oldham.

    Fractional Calculus generalises the integration and differential operators.

    For example have you ever wondered what [tex]\frac{d^{\frac{1}{2}}}{dx^{\frac{1}{2}}}[/tex] would stand for?

    The book covers the theory and its application as I can remmber in stuff like diffusion equations and other stuff.
     
  4. Sep 12, 2010 #3
    I see, a complete answer would be appreciated.. what prerequisites I need to know to learn fractional calculus? do I need to have mastered partial differential equations to learn fractional calculus topics?
     
  5. Sep 12, 2010 #4
  6. Sep 12, 2010 #5

    MathematicalPhysicist

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    Well, the first few chapters you don't need more than Calculus 2-3 (chapter 1-5), chapters 6-7, it can be a plus if you have been exposed to ODE and special functions, the rest you really do need to know good PDE especially the last chapter which deals with diffusion.
     
  7. Sep 12, 2010 #6
    I first learned of it in a PDE course dealing with Sobolev spaces. Real Analysis by Folland and PDE by Evans both have a decent introduction in the latter part of the books. Folland gives the information to understand it in the previous part (though I found Folland to be quite difficult unless you already have a decent Reals background).
     
  8. Sep 13, 2010 #7
    Not so much. Of course, you need to master Riemann integration. Riemann-Liouville Integral transform isn't more difficult than many other integral transforms, like Laplace-, Fourier-, etc.
     
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