IJPAM: Volume 37, No. 3 (2007)
SYMBOLIC DERIVATIVES AND INTEGRALS OF
THE POWER-EXPONENTIAL CLASS
Department of Mathematics and Statistics
Montreal, Quebec, H3G 1M8, CANADA
e-mails: email@example.com, firstname.lastname@example.org
Abstract.We give a complete solution to the problem of symbolic differentiation and integration of arbitrary (integer, fractional, or real) order of the power-exponential class
In Maple, the formulas correspond to invoking the commands , for differentiation and for integration, where is an integer, a fraction, a real, or a symbol. They enhance the ability of computer algebra systems for computing derivatives and integrals of arbitrary orders at a point .
The arbitrary order of differentiation is found according to the Riemann-Liouville definition, whereas the generalized Cauchy -fold integral is adopted for arbitrary order of integration.
One of the key points in this work is that the approach does not
depend on integration techniques.
Received: March 26, 2007
AMS Subject Classification: 26A33
Key Words and Phrases: fractional derivatives, fractional integrals, -function, -function
Source: International Journal of Pure and Applied Mathematics