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1

Non-differentiable Solutions for Local Fractional Nonlinear Riccati Differential Equations

Yang X.-J., Srivastava H. M., Torres D. F. M., Zhang Y.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

409--417

EN

We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFNRDE with constant coefficients is considered and non-differentiable solutions for special cases obtained.

2

A New Family of the Local Fractional PDEs

Yang X.-J., Machado J. A. T., Nieto J. J.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

63--75

EN

A new family of the local fractional PDEs is investigated in this article. The linear, quasilinear, semilinear and nonlinear local fractional PDEs are presented. Furthermore, three types of the local fractional PDEs are discussed, namely, parabolic, hyperbolic and elliptic. Several examples illustrate the corresponding models in nonlinear mathematical physics.

3

A study of critical point instability of micro and nano beams under a distributed variable-pressure force in the framework of the inhomogeneous non-linear nonlocal theory

Rahimi Z., Rezazadeh G., Sumelka W., Yang X.-J.

Archives of Mechanics

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2017

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Vol. 69, nr 6

413--433

EN

Fractional derivative models (FDMs) result from introduction of fractional derivatives (FDs) into the governing equations of the differential operator type of linear solid materials. FDMs are more general than those of integer derivative models (IDMs) so they are more fixable to describe physical phenomena. In this paper the inhomogeneous nonlocal theory has been introduced based on conformable fractional derivatives (CFD) to study the critical point instability of micro/nano beams under a distributed variable-pressure force. The phase of distributed variable-pressure force is used for electrostatic force, electromagnetic force and so on. This model has two free parameters: i) parameter to control the order of inhomogeneity in constitutive relations that gives a general form to the model, and ii) a nonlocal parameter to consider size dependence effects in micron and sub-micron scales. As a case study the theory has been used to model micro cantilever (C-F) and doubly-clamped (C-C) silicon beams under a distributed uniform electrostatic force in the presence of von-Karman nonlinearity and their static critical point (static pull-in instability), moreover, effects of different inhomogeneity have been shown on the pull-in instability.

4

Simultaneous RP-LC analysis of 10-O-(N,N-dimethylaminoethyl)-ginkgolide B and three related impurities

Liu W.-Y, Yang X.-J, Li P., Feng F, Mao L.

Acta Chromatographica

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2011

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Vol. 23, no. 3

459--468

EN

10-O-(N,N-dimethylaminoethyl)-ginkgolide B (XQ-1) is an intermediate for synthesizing 10-O-(N,N-dimethylaminoethyl)-ginkgolide B methanesulfonate (XQ-1H), which is a novel ginkgolide B derivative and is being developed as a platelet-activating factor antagonist. A specific and rapid liquid chromatographic method was developed for the quantitative analysis of XQ-1 and its three related impurities, which were 10-O-(N,N-dimethylaminoethyl)-11,12-seco-ginkgolide B (imp-1), 10-O-(N,N-dimethylaminoethyl)-11,12-seco-3,14-dehydroginkgolide B (imp-2) and 10-O-(N,N-dimethylaminoethyl)-3,14-dehydroginkgolide B (imp-3) simultaneously in XQ-1 samples. Chromatographic separation was achieved on a CN band stationary phase, with the mobile phase consisting of methanol and 20 mM dipotassium hydrogen phosphate (pH 7.5) (50:50, υ/υ) in isocratic elution. The flow rate was 1.0 mL min-1 and detector was set at 220 nm. The method was optimized by the analysis of the samples generated during the forced degradation studies. The XQ-1, imp-1, imp-2, and imp-3 were completely separated within 15 min. The resolutions (Rs) amongst four target compounds were >2. The developed method was validated with respect to specificity, linearity, accuracy, precision, and robustness. The results indicated that the simultaneous LC determination method was readily utilized as a quality control method for XQ-1 sample.