Dear researchers:
Recently, many articles have been published in the area of finding exact solutions of fractional nonlinear PDEs by applying a fractional transformation that convert the fraction problem into integer-derivative case (for example \frac{ t^{\alpha}}{\Gamma(\alpha)} to be replaced by \tau), then applying solitary wave methods to obtain exact solutions in \tau. Then, remove \tau from the final result and replace it by \frac{ t^{\alpha}}{\Gamma(\alpha)} . I wonder? Does the fractional derivative deform the shape of the solution using this process. I believe adopting such scheme is killing the effect of fractional-derivative.
It would be great if some one can clarify this issue.
Thanks
D^alpha [f(u(x))]=f'(u)*D^alpha[u(x)] .
This is my concern that Jumarie's acts like integer-derivative! it makes fractional calculus looks like classical. On the other side, conformable derivative it seems similar to Jumarie's.
Sure, I hope to collaborate for a good work soon.
Best regards
Jumarie's fractional derivative is suggested to satisfy the Leibniz's chain rule. However, it has been proved by Tarasov that the Jumarie's fractional derivatives cannot be considered as derivatives of non-integer order, since the Leibniz chain rule holds only for first order derivatives.
Conformable derivative seem similar to Jumarie one...
Regards.
- Badges
- Science topic