Hello Mboh,

Apologies but there isn't very much information in your query to clarify what it is your after (in terms of the applications). Also by fractional differential equations are you referring to ODE or PDE?

I have added a couple of papers below that may be of some help or at least give you a direction to move towards in order to further your research.

Physical applications of fixed point methods in differential equations by Chris Albert. https://math.uchicago.edu/~may/REU2019/REUPapers/Albert.pdf

Fixed point results with applications to fractional differential equations of anomalous diffusion by Z. Ma et al.

https://www.mdpi.com/2504-3110/8/6/318

I hope this helps.

Marc