Meaning of fractional calculus | Babel Free

Definitions

The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus.

uncountable

Equivalents

Examples

“2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12, The paper presents the definition sets required for initialized fractional calculi. Two underlying bases have been used, the Riemann-Liouville based fractional calculus and the Grünwald based functional calculus (by reference).”

“One of the major advantages of fractional calculus is that it can be considered as a superset of integer-order calculus. Thus fractional calculus has the potential to accomplish what integer-order calculus cannot. We believe that many of the great future developments will come from the applications of fractional calculus to different fields.”

“This chapter presents a number of functions that have been found to be useful in providing solutions to the problems of fractional calculus. […]The Mittag-Leffler function is the basis function to functional calculus, as the exponential function is to the integer-order calculus.”

CEFR level