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The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

The fractional derivative of f(t) of order mu>0 (if it exists) can be defined in terms of the fractional integral D^(-nu)f(t) as D^muf(t)=D^m[D^(-(m-mu))f(t)], (1) where m is ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

Denote the nth derivative D^n and the n-fold integral D^(-n). Then D^(-1)f(t)=int_0^tf(xi)dxi. (1) Now, if the equation D^(-n)f(t)=1/((n-1)!)int_0^t(t-xi)^(n-1)f(xi)dxi (2) ...

Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...

The solution to the differential equation [D^(2v)+alphaD^v+betaD^0]y(t)=0 (1) is y(t)={e_alpha(t)-e_beta(t) for alpha!=beta; ...

A transformation of the form w=f(z)=(az+b)/(cz+d), (1) where a, b, c, d in C and ad-bc!=0, (2) is a conformal mapping called a linear fractional transformation. The ...

The maximum possible weight of a fractional clique of a graph G is called the fractional clique number of G, denoted omega^*(G) (Godsil and Royle 2001, pp. 136-137) or ...