Sentence examples for by using the fractional from inspiring English sources

Simulation results are obtained by using the Fractional Order PI controller are better than the ones are obtained by using the Integer Order PI controller.

The effects of relevant parameters, namely; ultrasound power, temperature, time, activated carbon concentration, dye concentration and initial pH have been investigated on the decolorization and COD reduction by using the fractional factorial design and the orthogonal central composite design.

By using the fractional Fourier transform (FrFT) operator with the optimal order, the proposed time-domain dynamical system is transformed into the equivalent FrFT-domain system driven by the periodic signal and noise.

In this paper, we propose a new method to quickly generate near optimum feasible (integer) solutions by using the fractional solutions from the linear programming (LP) relaxation of the IP model.

Sub-pixel mapping is a promising technique for producing a spatial distribution map of different categories at the sub-pixel scale by using the fractional abundance image as the input.

As applications, by using the fractional Birkhoffian method, we construct four kinds of actual fractional dynamical models, which include a fractional Duffing oscillator model, a fractional Whittaker model, a fractional Emden model and a fractional Hojman Urrutia model, and we explore the equilibrium stability of these models respectively.

Some novel sufficient conditions for chaos synchronization of fractional-order chaotic systems with model uncertainties and external disturbances are derived by using the fractional-order extension of the Lyapunov stability theorem.

In this paper, we deal with a class of nonlinear fractional nonautonomous evolution equations with delay by using the Hilfer fractional derivative, which generalizes the famous Riemann-Liouville fractional derivative.

In this paper, we deal with a class of nonlinear fractional differential equations of Sobolev type with boundary conditions by using the Hilfer fractional derivative, which generalizes the famous Riemann Liouville fractional derivative.

In [12], Liao et al. gave the existence theorem of solutions for fractional impulsive neutral functional differential equations with infinite delay by using the Caputo fractional derivative, Hausdorff's measure of noncompactness and the theory of Mönch.

The effect of some parameters such as temperature, stirring speed, H3BO3-to-ZnO ratio, % seed crystal/(H3BO3 + ZnO) and time was studied on zinc borate production by using the 25−1 fractional factorial design and central composite design methods.