Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. Two-dimensional nonlinear system with one output function that depends only on one state variable is studied in detail. Viscoelastic and Disordered Media: Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-displacement, by H. The guest editors hope that this collection of papers may be useful and fruitful for scholars, researchers and advanced technical members of industrial laboratory facilities, for developing new tools and products. These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances.
Narahari Achar; The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equations, by B. Ozkan;Towards integrated nanoelectronic and photonic devices, by Alexander Quandt, Maurizio Ferrari and Giancarlo C. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. We confirm these results in the E-K case and illustrate our considerations with numerical examples. The developed fractional-order controller does not require the knowledge about both the interval of uncertain parameters and the upper bound of the additive disturbance. Moreover, a kind of explicit power series solutions of the equation is derived by virtue of the power series theory.
To help one discover mystery in complex systems, the newest developments in such fields should be disseminated in the community of science and technology. This work studies the fractional dynamics of an ultracapacitor which is used in a Buck-Boost power electronic converter as energy storage unit. Topological properties such as boundedness and compactness are studied in different spaces. Potential topics included, but are not limited to: Local fractional integral transforms and applications Local fractional differential equations and applications Local fractional integral equations with their solutions Existence and uniqueness of solutions of local fractional differential equations Analytical, approximate and numerical, exact solutions of local fractional differential equations Local fractional inequalities Advanced applications of local fractional calculus Fractal geometry Applications of fractal theory in science and engineering Authors are welcome to contact the Lead Guest Editor, Dr. To solve this problem, a new nonlinear adaptive control law is constructed via fractional-order backstepping scheme.
Ultracapacitors display long-term transients lasting for many months. Stability of impulsive fractional-order systems is investigated in this paper. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann—Liouville fractional derivative. A recovery study with the synthetic mixtures was carried out and the obtained results were highly satisfactory. Finally, one illustrative example is given to demonstrate the theoretical results. The adaptation law will be constructed from a sliding surface via gradient method. We present two examples to show the applicability of our results.
Recent advances in local fractional calculus, such as local fractional differential equations and integral equations, inequalities, fractal sets, fractal metric space, fractal Banach space, fractal Hilbert space and others, demonstrate its usefulness in theoretical and real-world applications. Note that fractional operators also provide an alternative method to the classical models including dilate terms. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Then, based on such comparison principles, sufficient conditions for the Mittag-Leffler stability of impulsive fractional-order systems are established. In this work, the fractional behaviour of the ultracapacitor used in the Buck-Boost converter has been identified by means of an experimental test. Numerical results confirm the accuracy and efficiency of the proposed scheme.
Classical second derivative method was applied to the fractional wavelet signals in the wavelet domain. The amounts of trimethoprim and sulfachloropyridazine sodium in tablets. In the paper minimum energy control problem of infinite-dimensional fractional-discrete time linear systems is addressed. In-plane free vibration and stability analysis of high speed rotating disks and rings. In order to illustrate the procedure for the controllers design and application, several simulations and practical tests on the velocity and position control of the servo are given. The main of this chapter is dedicated to do a first approach to show how introduce Fractional Models only under a deterministic basement. Simulation results show that the desired specifications are fulfilled and the fractional controller is robust in comparison with classical controller.
For example, in order to examine the stability of fractional-delay systems, the location of the poleson the first Riemann sheet should be known since the stability is related to thepoles that are located on the right half-plane of the first Riemann sheet. In this article, we obtain the viscous damping coefficient β theoretically and experimentally in the spring-mass-viscodamper system. From the results, it can be obtained that the use of the fractional predictive controller lets the system get a good performance and offers a set of controlled systems with different dynamics. Additionally, existence and uniqueness of the solution are discussed by employing the Picard-Lindelöf scheme. The classical models are recovered when the order of the fractional derivatives is equal to 1.
Deadline for final decision notification: October 30, 2018. An adaptive fractional-order controller has been designed to synchronize two identical chaotic systems. Singh, Miroslav Penchev, Xiaoye Jing, Alfredo A. Good agreement between them is confirmed. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion.