323,511 research outputs found
Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type
No full textThe paper [5] by R. Garrappa, S. Rogosin, and F. Mainardi, entitled "On a generalized three-parameter Wright function of the Le Roy type" and published in Fract. Calc. Appl. Anal. 20 (2017), 1196-1215, ends up leaving the open question concerning the range of the parameters alpha, beta and. for which Mittag-Leffler functions of Le Roy type F-alpha, beta((gamma)) are completely monotonic. Inspired by the 1948 seminal H. Pollard's paper which provides the proof of the complete monotonicity of the one-parameter Mittag-Leffler function, the Pollard approach is used to find the Laplace transform representation of F-alpha, beta((gamma)) for integer gamma = n and rational 0 < alpha <= 1/n. In this way it is possible to show that the Mittag-Leffler functions of Le Roy type are completely monotone for a = 1/n and beta >= (n + 1)/(2n) as well as for rational 0 < alpha <= 1/2, beta = 1 and n = 2. For further integer values of n the complete monotonicity is tested numerically for rational 0 < alpha < 1/n and various choices of beta. The obtained results suggest that for the complete monotonicity the condition beta >= (n + 1)/(2n) holds for any value of n
A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation
No full textWe consider an initial-boundary-value problem for a time-fractional diffusion equation with initial condition u0(x) and homogeneous Dirichlet boundary conditions in a bounded interval [0, L]. We study a semidiscrete approximation scheme based on the pseudo-spectral method on Chebyshev-Gauss-Lobatto nodes. In order to preserve the high accuracy of the spectral approximation we use an approach based on the evaluation of the Mittag-Leffler function on matrix arguments for the integration along the time variable. Some examples are presented and numerical experiments illustrate the effectiveness of the proposed approac
Neuroadaptive Optimal Fixed-Time Synchronization and Its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems
No full textThis article investigates the neuroadaptive optimal fixed-time synchronization and its circuit realization along with dynamical analysis for unidirectionally coupled fractional-order (FO) self-sustained electromechanical seismograph systems under subharmonic and superharmonic oscillations. The synchronization model of the coupled FO seismograph system is established based on drive and response seismic detectors. The dynamical analysis reveals this coupled system generating transient chaos and homoclinic/heteroclinic oscillations. The test results of the constructed equivalent analog circuit further testify its complex nonlinear dynamics. Then, a neuroadaptive optimal fixed-time synchronization controller integrated with the FO hyperbolic tangent tracking differentiator (HTTD), interval type-2 fuzzy neural network (IT2FNN) with transformation, and prescribed performance function (PPF) together with the constraint condition is developed in the backstepping recursive design. Furthermore, it is proved that all signals of this closed-loop system are bounded, and the tracking errors fall into a trap of the prescribed constraint along with the minimized cost function. Extensive studies confirm the effectiveness of the proposed scheme
An approach to optimal integer and fractional-order modeling of electro-injectors in compression-ignition engines
No full textThe automotive industry continuously spends resources to reduce fuel consumption, operating costs, and harmful emissions. Namely, regulations are becoming more restrictive and customers’ expectations are growing. To achieve these goals in compression-ignition engines, an approach employs innovative Common Rail Injection Systems, based on advanced control units and electro-injectors. The latter require an accurate model for optimizing layout and operation and for controlling injection rate shaping strategies that are fundamental for reducing consumption and emission. This work proposes a complete innovative electro-injector model, which integrates an integer-order representation of inner volumes and mechanical and electromagnetic elements, and a fractional-order model for the high-pressure fuel propagation inside a specific pipe in the injector. Fractional-order modeling of this complex process is motivated by the superior description ability of a fractional-order system with respect to an integer-order system. Then a new numerical method is proposed and tuned to simulate the system. A differential evolution technique optimizes the model parameters. Simulation results show that benefits are gained in model prediction capability
Dynamical analysis and accelerated optimal stabilization of the fractional-order self-sustained electromechanical seismograph system with fuzzy wavelet neural network
No full textThis paper investigates dynamical analysis and accelerated optimal stabilization issues of the fractional-order (FO) self-sustained electromechanical seismograph system under energy mechanism. The FO equation governing this system with gyroscopic coupling is established. Its dynamical analysis, based on phase diagrams and Lyapunov exponents, shows that chaotic and periodic behaviors strongly depend on physical parameters and on the values of the FOs. In accelerated feedforward controller, a shaping behavior function (SBF) is used to accelerate tracking error convergence at controllable rate and time, a fuzzy wavelet neural network (FWNN) with transformation is employed to approximate unknown functions of system, and a tracking differentiator is set to solve issue from complexities of SBF and FO under the framework of FO backstepping. In optimal feedback controller, an adaptive dynamic programming strategy is proposed to deal with a zero sum differential game solution problem, wherein the FWNN is employed to approximate the solution of the constrained Hamilton–Jacobi-Isaacs equation online. Furthermore, it is testified that all signals of the closed-loop system are bounded by using barrier Lyapunov function and the constrained conditions are not violated along with the cost function being minimized. Numerical simulation proves the effectiveness and advantages of the proposed scheme
On a generalized three-parameter wright function of le Roy type
No full textRecently S. Gerhold and R. Garra - F. Polito independently introduced a new function related to the special functions of the Mittag-Leffler family. This function is a generalization of the function studied by Le Roy in the period 1895-1905 in connection with the problem of analytic continuation of power series with a finite radius of convergence. In our note we obtain two integral representations of this special function, calculate its Laplace transform, determine an asymptotic expansion of this function on the negative semi-axis (in the case of an integer third parameter Î3) and provide its continuation to the case of a negative first parameter. An asymptotic result is illustrated by numerical calculations. Discussion on possible further studies and open questions are also presented
On some inequalities for the two-parameter Mittag-Leffler function in the complex plane
No full textFor the two-parameter Mittag-Leffler function Eα,β with α>0 and β≥0, we consider the question whether |Eα,β(z)| and Eα,β(Rz) are comparable on the whole complex plane. We show that the inequality |Eα,β(z)|≤Eα,β(Rz) holds globally if and only if Eα,β(−x) is completely monotone on (0,∞). For α∈[1,2) we prove that the complete monotonicity of 1/Eα,β(x) on (0,∞) is necessary for the global inequality |Eα,β(z)|≥Eα,β(Rz), and also sufficient for α=1. For α≥2 we show that the absence of non-real zeros for Eα,β is sufficient for the global inequality |Eα,β(z)|≥Eα,β(Rz), and also necessary for α=2. All these results have an explicit description in terms of the values of the parameters α,β. Along the way, several inequalities for Eα,β on the half-plane {Rz≥0} are established, and a characterization of its log-convexity and log-concavity on the positive half-line is obtained
Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial
No full textSeveral fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly used operators and illustrated two approaches to generalize integer-order derivatives to fractional order; the aim was to provide a tool for a full understanding of the specific features of each fractional derivative and to better highlight their differences. We hence provided a guide to the evaluation of fractional integrals and derivatives of some elementary functions and studied the action of different derivatives on the same function. In particular, we observed how Riemann−Liouville and Caputo’s derivatives converge, on long times, to the Grünwald−Letnikov derivative which appears as an ideal generalization of standard integer-order derivatives although not always useful for practical applications
Diffusive author(s), cohesive author: Analysis of S/N (1994)
No full textThis study indicates the ways in which various aspects of the author(s) are brought forth in Dumb type’s performance art, the S/N production. Previous research has suggested a non-hierarchical organization of Dumb type and the absence of a “privileged author” in Dumb type’s collaborative work, S/N. However, the results that I have investigated from member’s interviews on the creative process of S/N along with my analysis of the recorded images of S/N, indicate a different aspect of the author(s). First, S/N was created through, so to speak, the collective ideas of the members of Dumb type. Further, S/N has at least nine quotations from previous performances, installations, and printed writings, besides the work-in-progress technique. Explicating one of the “author functions” as given by Michel Foucault, each text has plural subjects of the author. However, it has been revealed from members’ interviews that Teiji Furuhashi had a decision-making role in selecting the members’ ideas within the performance. Since then, S/N has had plural subjects of creation; however, Furuhashi is one of the subjects of creation along with the “privileged author.” S/N has plural authors (diffusive authors) yet at the same time, it has a “privileged author,” Teiji Furuhashi (cohesive author)
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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