I am not an expert in RBF but also interested in using it for fractional differential equations. I also read about it and could see potential research work using it.
We have worked with RBFs and published some ideas in applying them in forward and inverse dynamical problems. Please see attached papers and it would be a pleasure discussing them further with you.
Article Time Domain Inverse Problems in Nonlinear Systems Using Coll...
Article A Simple, Fast, and Accurate Time-Integrator for Nonlinear D...
It is interesting to see people working in this area. I am encouraged to continue looking into it especially the applications into fractional differential equations.
I am also working in RBF based meshless methods for PDEs. Let me know your query and I will be happy If I could help. I will be happy to collaborate. ( I wont call myself an expert though).