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Keywords: Numerical approach Fractional calculus Fractional differential equations Piecewise interpolation Simpson method a b s t r a c t Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical… (More)

- Leizhen Cai, Junjie Ye
- MFCS
- 2014

Let G be an edge-bicolored graph where each edge is colored either red or blue. We study problems of obtaining an induced subgraph H from G that simultaneously satisfies given properties for H's red graph and blue graph. In particular, we consider Dually Connected Induced Subgraph problem — find from G a k-vertex induced subgraph whose red and blue graphs… (More)

- Leizhen Cai, Junjie Ye
- WG
- 2016

We consider the problem of finding, for two pairs (s1, t1) and (s2, t2) of vertices in an undirected graphs, an (s1, t1)-path P1 and an (s2, t2)-path P2 such that P1 and P2 share no edges and the length of each Pi satisfies Li, where Li ∈ {≤ ki, = ki, ≥ ki, ≤ ∞}. We regard k1 and k2 as parameters and investigate the parameterized complexity of the above… (More)

For an edge-bicolored graph G where each edge is colored either red or blue, a vertex set S is a dual feedback vertex set if S hits all blue cycles and red cycles of G. In this paper, we show that a dual feedback vertex set of size at most k can be found in time O * (c k 1) and all minimal dual feedback vertex set of size at most k can be enumerated in time… (More)

- Leizhen Cai, Junjie Ye
- AAIM
- 2014

This article presents a numerical technique for computing the biaxial yield surface of polymer-matrix composites with a given microstructure. Generalized Method of Cells in combination with an Improved Bodner-Partom Viscoplastic model is used to compute the inelastic deformation. The validation of presented model is proved by a fiber Bragg gratings (FBGs)… (More)

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