Asymptotic approximations for non-integer order derivatives of monomials

Abstract

In this note, we develop new, simple and very accurate asymptotic approximations for non-integer order derivatives of monomial functions by using the more accurate asymptotic approximations for large factorials that have recently appeared in the literature.

Keywords:

• monomial functions
• fractional derivative
• gamma function
• asymptotic approximation
• Stirling's formula
• Burnside's formula

Mathematics Subject Classification (2010):

• 41A60

Acknowledgements

I wish to thank my colleagues in the Department of Mathematics and Statistics at the Federal Polytechnic, Bida for their patience and understanding in listening to my presentations during the initial preparations of this work.

Additional information

Funding

This work was financially supported in part by the management of the Federal Polytechnic, Bida, on the recommendations of its Research, Conferences and Publications Committee (RC&PC).