Sentence examples for discrete calculus from inspiring English sources

This suggests that a unique exact discrete calculus does not exist.

Hilger [2] introduced the notion of time scales in order to unify the theory of continuous and discrete calculus.

Analysis on measure chains was initiated by Stefan Hilger [1] as a bridge between continuous and discrete calculus.

If, then delta derivative is from continuous calculus; if, the delta derivative is the forward difference,, from discrete calculus.

The discrete calculus analysis allows a generalization of the Keller Box scheme to non-simplectic meshes to be constructed.

Stefan Hilger [1] introduced the notion of time scale in 1988 in order to unify the theory of continuous and discrete calculus.

In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus.

The theory of fractional h-discrete calculus is a rapidly developing area of great interest both from a theoretical and applied point of view.

The main aim of this paper is to establish the h-analogue of the classical Hardy-type inequality (1.1) in fractional h-discrete calculus with sharp constants which is another discrete analogue of inequality (1.1).

The suggested method is the development of Podlubny's matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359–386].

First of all, for a general overview of the discrete fractional calculus, together with substantial background on the integer-order difference calculus, we direct the interested reader to the textbook by Goodrich and Peterson [3].