This study constructs a novel four-dimensional fractional-order chaotic system. It verifies chaotic nonlinear dynamic behaviors and physical reliability by numerical simulation and hardware circuit design. For a class of parameter uncertainty fractional different-lags ( i ) chaotic systems, the authors design a time-delayed ( ) synchronization controllers and parameter adaptive laws. It proves ...

We firstly give a modification of the known Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function. We secondly establish several Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function. The results presented here, being very general, are p...

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

A graph G is fractional ID-[a, b]-factor-critical if G − I has a fractional [a, b]-factor for every independent set I of G. We extend a result of Zhou and Sun concerning fractional ID-k-factor-critical graphs.

For any k ∈ N, the k−subdivision of graph G is a simple graph G 1 k , which is constructed by replacing each edge of G with a path of length k. In this paper we introduce the mth power of the n−subdivision of G, as a fractional power of G, denoted by G m n . In this regard, we investigate chromatic number and clique number of fractional power of graphs. Also, we conjecture that χ(G m n ) = ω(G ...

In a companion paper we characterized the class of scale-invariant convolution operators: the generalized fractional derivatives of order γ. We used these operators to specify regularization functionals for a series of Tikhonov-like least squares data fitting problems and proved that the general solution is a fractional spline of twice the order. We investigated the deterministic properties of ...

We study the complexity of computing equilibria in two classes of network games based on flows fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet together and hence its stability, i.e. the equilibria of fractional BGP games [15], is a matter of practical importance. BBC games [21] follow in the tradition o...

We prove that for any positive integer k and for ε = 1/((k + 2)(3k2 + 1)), the edges of any graph whose fractional arboricity is at most k + ε can be decomposed into k forests and a matching.

The fractional parts of the Bernoulli numbers are dense in the interval (0, 1). For every positive integer k, the set of all m for which B 2. has the same fractional part as B 21 has positive asymptotic density .

We study the following problem: given a real number k and an integer d, what is the smallest ε such that any fractional (k+ε)-precoloring of vertices at pairwise distances at least d of a fractionally k-colorable graph can be extended to a fractional (k+ ε)coloring of the whole graph? The exact values of ε were known for k ∈ {2} ∪ [3,∞) and any d. We determine the exact values of ε for k ∈ (2, ...