fractional calculus

Noun

fractional calculus (countable and uncountable, plural fractional calculi)

1. (uncountable) 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.
   • 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).2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12
   • 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...2007, J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado, editors, Advances in Fractional Calculus, Springer, page xii