Is there any explanation about the following : The Riemann liouville fractional derivative is mostly used by mathematicians but this approach is not suitable for real -world physical problems since it requires the definition of fractional order initial conditions ,which have no physically meaningful explanation yet . If there is any explanation I will be very thankful.

  • $\begingroup$ What is there to explain? It seems like it says everything necessary. $\endgroup$ – Cameron Williams Jun 15 '17 at 12:58
  • $\begingroup$ Yes . I think it's just one idea $\endgroup$ – user449609 Jun 15 '17 at 12:59
  • $\begingroup$ Really it traces back to us not knowing what fractional derivatives really are in the real world. They're nonlocal and bizarre. To make matters worse, fractional initial conditions are totally strange. That said, there is a lot of work being done on fractional calculus applied to the real world. I suspect at least in certain examples that these things are understood, but not in any sort of generality. $\endgroup$ – Cameron Williams Jun 15 '17 at 13:04
  • $\begingroup$ I think I once heard from a mathematician that the topic of "supersymmetry" in physics makes use of fractional derivatives. I cannot provide any references as this is a vague memory of an off-hand comment. $\endgroup$ – user52969 Jun 15 '17 at 13:05
  • $\begingroup$ There are fractional Schrodinger equations, Levy flights involve fractional derivatives, fractional calculus can be used in electrochemistry, they show up in some seismic and signal processing applications. It's somewhat fringe insofar that it isn't widespread but gaining popularity. $\endgroup$ – Cameron Williams Jun 15 '17 at 13:09

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