Non-integer order differentiation and their approximations via Laplace transformation
This thesis shows existence and new approximation methods to fractional derivatives of continuous and exponentially bounded functions provided the Laplace transform of the integer-order derivative satisfies a growth condition. It is shown that, under this condition, the fractional derivative exists and it is continuous and exponentially bounded. New approximation methods for fractional derivatives are obtained based on the Rational Inversion of the Laplace Transform. Examples are provided for the fractional derivatives of the exponential, sine, and cosine functions.
Fedrick Nicholas Reynolds,
"Non-integer order differentiation and their approximations via Laplace transformation"
ETD Collection for Tennessee State University.