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Relevant bibliographies by topics / Fractional Scheme Theory

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Academic literature on the topic 'Fractional Scheme Theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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Journal articles on the topic "Fractional Scheme Theory"

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Vafaei, Vajiheh, Hossein Kheiri, and Aliasghar Jodayree Akbarfam. "‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎." Boletim da Sociedade Paranaense de Matemática 39, no. 5 (2021): 57–72. http://dx.doi.org/10.5269/bspm.41252.

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In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to ver

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Zhou, Ping, Rui Ding, and Yu-xia Cao. "Hybrid Projective Synchronization for Two Identical Fractional-Order Chaotic Systems." Discrete Dynamics in Nature and Society 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/768587.

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A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchronization for the fractional-order Chen chaotic system and hybrid projective synchronization for the fractional-order hyperchaotic Lu system are used to demonstrate the validity and feasibility of the pro

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Zhou, Ping, and Rui Ding. "Modified Function Projective Synchronization between Different Dimension Fractional-Order Chaotic Systems." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/862989.

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A modified function projective synchronization (MFPS) scheme for different dimension fractional-order chaotic systems is presented via fractional order derivative. The synchronization scheme, based on stability theory of nonlinear fractional-order systems, is theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

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WANG, XING-YUAN, ZUN-WEN HU, and CHAO LUO. "GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS." International Journal of Modern Physics B 27, no. 30 (2013): 1350195. http://dx.doi.org/10.1142/s0217979213501956.

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In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the

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WANG, XING-YUAN, and ZUN-WEN HU. "PROJECTIVE SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS BASED ON STATE OBSERVER." International Journal of Modern Physics B 26, no. 30 (2012): 1250176. http://dx.doi.org/10.1142/s0217979212501767.

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Based on the stability theory of fractional order systems and the pole placement technique, this paper designs a synchronization scheme with the state observer method and achieves the projective synchronization of a class of fractional order chaotic systems. Taking an example for the fractional order unified system by using this observer controller, and numerical simulations of fractional order Lorenz-like system, fractional order Lü system and fractional order Chen system are provided to demonstrate the effectiveness of the proposed scheme.

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Hu, Shaoxiang. "External Fractional-Order Gradient Vector Perona-Malik Diffusion for Sinogram Restoration of Low-Dosed X-Ray Computed Tomography." Advances in Mathematical Physics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/516919.

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Existing fractional-order Perona-Malik Diffusion (FOPMD) algorithms are defined as fully spatial fractional-order derivatives (FSFODs). However, we argue that FSFOD is not the best way for diffusion since different parts of spatial derivative play different roles in Perona-Malik diffusion (PMD) and derivative orders should be decided according to their roles. Therefore, we adopt a novel fractional-order diffusion scheme, named external fractional-order gradient vector Perona-Malik diffusion (EFOGV-PMD), by only replacing integer-order derivatives of “external” gradient vector to their fraction

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Xin, Baogui, and Tong Chen. "Projective Synchronization ofN-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control." Discrete Dynamics in Nature and Society 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/191063.

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Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-o

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Abdel-Rehim, Entsar A. "The Approximate and Analytic Solutions of the Time-Fractional Intermediate Diffusion Wave Equation Associated with the Fokker–Planck Operator and Applications." Axioms 10, no. 3 (2021): 230. http://dx.doi.org/10.3390/axioms10030230.

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In this paper, the time-fractional wave equation associated with the space-fractional Fokker–Planck operator and with the time-fractional-damped term is studied. The concept of the Green function is implemented to drive the analytic solution of the three-term time-fractional equation. The explicit expressions for the Green function G3(t) of the three-term time-fractional wave equation with constant coefficients is also studied for two physical and biological models. The explicit analytic solutions, for the two studied models, are expressed in terms of the Weber, hypergeometric, exponential, an

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Zhang, Ruoxun, Yongli Liu, and Shiping Yang. "Adaptive Synchronization of Fractional-Order Complex Chaotic system with Unknown Complex Parameters." Entropy 21, no. 2 (2019): 207. http://dx.doi.org/10.3390/e21020207.

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This paper investigates the problem of synchronization of fractional-order complex-variable chaotic systems (FOCCS) with unknown complex parameters. Based on the complex-variable inequality and stability theory for fractional-order complex-valued system, a new scheme is presented for adaptive synchronization of FOCCS with unknown complex parameters. The proposed scheme not only provides a new method to analyze fractional-order complex-valued system but also significantly reduces the complexity of computation and analysis. Theoretical proof and simulation results substantiate the effectiveness

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Zhang, Feng, and Yang. "Complex Modified Projective Synchronization of Fractional-Order Complex-Variable Chaotic System with Unknown Complex Parameters." Entropy 21, no. 4 (2019): 407. http://dx.doi.org/10.3390/e21040407.

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This paper investigates the problem of complex modified projective synchronization (CMPS) of fractional-order complex-variable chaotic systems (FOCCS) with unknown complex parameters. By a complex-variable inequality and a stability theory for fractional-order nonlinear systems, a new scheme is presented for constructing CMPS of FOCCS with unknown complex parameters. The proposed scheme not only provides a new method to analyze fractional-order complex-valued systems but also significantly reduces the complexity of computation and analysis. Theoretical proof and simulation results substantiate

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Dissertations / Theses on the topic "Fractional Scheme Theory"

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Eliustaoglu, Esra. "INVESTIGATION OF FRACTION SCHEMES AND MODELS AS A MEANS TO UNDERSTAND HOW SIXTH GRADE STUDENTS MAKE SENSE OF FRACTIONS." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460137024.

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Books on the topic "Fractional Scheme Theory"

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. American Mathematical Society, 2014.

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Schwartz, Richard Evan. The Plaid Model. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691181387.001.0001.

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Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. This book provides a combinatorial model for orbits of outer billiards on kites. The book relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid

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Vurgaftman, Igor, Matthew P. Lumb, and Jerry R. Meyer. Bands and Photons in III-V Semiconductor Quantum Structures. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198767275.001.0001.

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Semiconductor quantum structures are at the core of many photonic devices such as lasers, photodetectors, solar cells etc. To appreciate why they are such a good fit to these devices, we must understand the basic features of their band structure and how they interact with incident light. This book takes the reader from the very basics of III-V semiconductors (some preparation in quantum mechanics and electromagnetism is helpful) and shows how seemingly obscure results such as detailed forms of the Hamiltonian, optical transition strengths, and recombination mechanisms follow. The reader does n

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Book chapters on the topic "Fractional Scheme Theory"

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Li, W., and S. Wang. "A 2nd-Order Numerical Scheme for Fractional Ordinary Differential Equation Systems." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_6.

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"- Approximation Schemes for Fractional Multicommodity Flow Problems." In Handbook of Graph Theory, Combinatorial Optimization, and Algorithms. Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/b19163-56.

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Tene, Alain Giresse, and Timoleon Crépin Kofane. "Novel Cryptography Technique via Chaos Synchronization of Fractional-Order Derivative Systems." In Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5418-9.ch013.

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Synchronization of fractional-order-derivative systems for cryptography purpose is still exploratory and despite an increase in cryptography research, several challenges remain in designing a powerful cryptosystem. This chapter addresses the problem of synchronization of fractional-order-derivative chaotic systems using random numbers generator for a novel technique to key distribution in cryptography. However, there is evidence that researchers have approached the problem using integer order derivative chaotic systems. Consequently, the aim of the chapter lies in coding and decoding a text via chaos synchronization of fractional-order derivative, the performance analysis and the key establishment scheme following an application on a text encryption using the chaotic Mathieu-Van Der Pol fractional system. In order to improve the level of the key security, the Fibonacci Q-matrix is used in the key generation process and the initial condition; the order of the derivative of the responder system secretly shared between the responder and the receiver are also involved. It followed from this study that compared to the existing cryptography techniques, this proposed method is found to be very efficient due to the fact that, it improves the key security.

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Tene, Alain Giresse, and Timoleon Crépin Kofane. "Novel Cryptography Technique via Chaos Synchronization of Fractional-Order Derivative Systems." In Research Anthology on Artificial Intelligence Applications in Security. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7705-9.ch097.

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Synchronization of fractional-order-derivative systems for cryptography purpose is still exploratory and despite an increase in cryptography research, several challenges remain in designing a powerful cryptosystem. This chapter addresses the problem of synchronization of fractional-order-derivative chaotic systems using random numbers generator for a novel technique to key distribution in cryptography. However, there is evidence that researchers have approached the problem using integer order derivative chaotic systems. Consequently, the aim of the chapter lies in coding and decoding a text via chaos synchronization of fractional-order derivative, the performance analysis and the key establishment scheme following an application on a text encryption using the chaotic Mathieu-Van Der Pol fractional system. In order to improve the level of the key security, the Fibonacci Q-matrix is used in the key generation process and the initial condition; the order of the derivative of the responder system secretly shared between the responder and the receiver are also involved. It followed from this study that compared to the existing cryptography techniques, this proposed method is found to be very efficient due to the fact that, it improves the key security.

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Tene, Alain Giresse, and Timoleon Crépin Kofane. "Novel Cryptography Technique via Chaos Synchronization of Fractional-Order Derivative Systems." In Research Anthology on Blockchain Technology in Business, Healthcare, Education, and Government. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-5351-0.ch045.

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Synchronization of fractional-order-derivative systems for cryptography purpose is still exploratory and despite an increase in cryptography research, several challenges remain in designing a powerful cryptosystem. This chapter addresses the problem of synchronization of fractional-order-derivative chaotic systems using random numbers generator for a novel technique to key distribution in cryptography. However, there is evidence that researchers have approached the problem using integer order derivative chaotic systems. Consequently, the aim of the chapter lies in coding and decoding a text via chaos synchronization of fractional-order derivative, the performance analysis and the key establishment scheme following an application on a text encryption using the chaotic Mathieu-Van Der Pol fractional system. In order to improve the level of the key security, the Fibonacci Q-matrix is used in the key generation process and the initial condition; the order of the derivative of the responder system secretly shared between the responder and the receiver are also involved. It followed from this study that compared to the existing cryptography techniques, this proposed method is found to be very efficient due to the fact that, it improves the key security.

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Tene, Alain Giresse, and Timoleon Crépin Kofane. "Novel Cryptography Technique via Chaos Synchronization of Fractional-Order Derivative Systems." In Research Anthology on Artificial Intelligence Applications in Security. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7705-9.ch097.

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Synchronization of fractional-order-derivative systems for cryptography purpose is still exploratory and despite an increase in cryptography research, several challenges remain in designing a powerful cryptosystem. This chapter addresses the problem of synchronization of fractional-order-derivative chaotic systems using random numbers generator for a novel technique to key distribution in cryptography. However, there is evidence that researchers have approached the problem using integer order derivative chaotic systems. Consequently, the aim of the chapter lies in coding and decoding a text via chaos synchronization of fractional-order derivative, the performance analysis and the key establishment scheme following an application on a text encryption using the chaotic Mathieu-Van Der Pol fractional system. In order to improve the level of the key security, the Fibonacci Q-matrix is used in the key generation process and the initial condition; the order of the derivative of the responder system secretly shared between the responder and the receiver are also involved. It followed from this study that compared to the existing cryptography techniques, this proposed method is found to be very efficient due to the fact that, it improves the key security.

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Ahmed, E., and Ahmed Ezzat Mohamed Matouk. "Fractional-Order Calculus in Antimicrobial Resistance and Waning Vaccination." In Advanced Applications of Fractional Differential Operators to Science and Technology. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-3122-8.ch001.

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In this chapter, a simple model for competition between drug resistant and drug sensitive bacteria is given. So, a model of antimicrobial resistance (AMR) and waning vaccination is presented. The model's steady states are obtained. The conditions of local stability of the equilibria are also derived via the fractional Routh-Hurwitz criterion. A discretization scheme has also been applied to the proposed fractional-order model to enhance the model's adequacy and accuracy of describing natural phenomena. So, dynamical behaviors of the resulting discrete-time model are studied such as local stability, existence of Neimark-Sacker, and flip bifurcations. Furthermore, existence of chaos in the discrete-time model is proved using the theorem given by Marotto. Chaotic attractors and routes to chaos are also depicted via various numerical tools.

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Hankin, David G., Michael S. Mohr, and Ken B. Newman. "Equal probability sampling." In Sampling Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198815792.003.0003.

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This chapter presents a formal quantitative treatment of material covered conceptually in Chapter 2, all with respect to equal probability with replacement (SWR) and without replacement selection simple random sampling, (SRS) of samples of size n from a finite population of size N. Small sample space examples are used to illustrate unbiasedness of mean-per-unit estimators of the mean, total and proportion of the target variable, y, for SWR and SRS. Explicit formulas for sampling variance indicate how estimator uncertainty depends on finite population variance, sample size and sampling fraction. Measures of the relative performance of alternative sampling strategies (relative precision, relative efficiency, net relative efficiency) are introduced and applied to mean-per-unit estimators used for the SWR and SRS selection methods. Normality of the sampling distribution of the SRS mean-per-unit estimator depends on sample size but also on the shape of the distribution of the target variable, y, values over the finite population units. Normality of the sampling distribution is required to justify construction of valid 95% confidence intervals that may be constructed around sample estimates based on unbiased estimates of sampling variance. Methods to calculate sample size to achieve accuracy objectives are presented. Additional topics include Bernoulli sampling (a without replacement selection scheme for which sample size is a random variable), the Rao–Blackwell theorem (which allows improvement of estimators that are based on selection methods which may result in repeated selection of the same units), oversampling and nonresponse.

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Townsend, Peter. "Musical Development Assisted by Technology." In The Evolution of Music through Culture and Science. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198848400.003.0002.

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In Europe, the first millennium life and music were tightly controlled by religion. Instruments were limited, with major differences between folk music for the masses, the aristocracy, and the church. Much early music was just a single line sung in unison. Progressions to several lines, chords, and the complexity of polyphony developed in parallel with written works and printing of religious and secular music. This liberating feature stimulated a wide range of new types of composition. By around 1600, there was an Italian explosion into opera and a major demand for secular music. Mathematicians devised a scheme of equal temperament tuning, which replaced the earlier ‘natural’ musical scales and this enabled keyboard instruments to play in any key. Low-cost printed music was widely available. Despite the volume of compositions, a relatively small fraction has survived as performance music in the present day and the reasons for this are mentioned.

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Soyata, Tolga, He Ba, Wendi Heinzelman, Minseok Kwon, and Jiye Shi. "Accelerating Mobile-Cloud Computing." In Cloud Technology. IGI Global, 2015. http://dx.doi.org/10.4018/978-1-4666-6539-2.ch090.

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With the recent advances in cloud computing and the capabilities of mobile devices, the state-of-the-art of mobile computing is at an inflection point, where compute-intensive applications can now run on today's mobile devices with limited computational capabilities. This is achieved by using the communications capabilities of mobile devices to establish high-speed connections to vast computational resources located in the cloud. While the execution scheme based on this mobile-cloud collaboration opens the door to many applications that can tolerate response times on the order of seconds and minutes, it proves to be an inadequate platform for running applications demanding real-time response within a fraction of a second. In this chapter, the authors describe the state-of-the-art in mobile-cloud computing as well as the challenges faced by traditional approaches in terms of their latency and energy efficiency. They also introduce the use of cloudlets as an approach for extending the utility of mobile-cloud computing by providing compute and storage resources accessible at the edge of the network, both for end processing of applications as well as for managing the distribution of applications to other distributed compute resources.

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Conference papers on the topic "Fractional Scheme Theory"

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Liu, Xiaojun, and Ling Hong. "Adaptive Synchronization of a Fractional-Order Complex T System With a Random Parameter." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46220.

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In this paper, the adaptive synchronization of a fractional-order complex T system with a random parameter is analyzed. Firstly, the Laguerre polynomial approximation method is applied to investigate the fractional-order system with a random parameter which obeys an exponential distribution. Based on this method, the stochastic system is reduced into the equivalent deterministic one. The improved Adams-Bashforth-Moulton algorithm with the predictor-correctors scheme is used to solve the approximately deterministic system numerically. Based on the stability theory of fractional-order systems, t

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Wang, Bin, Yangquan Chen, and Ying Yang. "Chattering-Free Finite-Time Stability of a Class of Fractional-Order Nonlinear Systems." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97674.

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Abstract This paper studies the chattering-free finite-time control for a class of fractional-order nonlinear systems. First, a class of fractional-order nonlinear systems with external disturbances is presented. Second, a new finite-time terminal sliding mode control method is proposed for the stability control of a class of fractional-order nonlinear systems by combining the finite-time stability theory and sliding mode control scheme. Third, by designing a controller with a differential form and introducing the arc tangent function, the chattering phenomenon is well suppressed. Additionally

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Xiros, Nikolaos I. "A Nonlinear Signal Analysis Scheme for Localization of a Moving Acoustic Source." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10763.

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The synthesis of coupled systems including linear propagation media and nonlinear lumped subsystems is investigated. The resulting coupled system is expected to exhibit improved dynamic behavior. Such improvements are sought after by designing exclusively the lumped nonlinear subsystem and not by modifying the propagation medium. The lumped subsystem can be static or dynamic as well as passive or active. The design method is based on the Volterra-Wiener theory of nonlinear systems combined with the Linear Fractional Transformation employed for the analysis of uncertain linear systems. Although

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Walters, D. Keith. "Application of High-Resolution Spatial Discretization Schemes to Volume-of-Fluid Simulations on Three-Dimensional Unstructured Meshes." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43965.

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The interface capturing approach to volume-of-fluid (VOF) simulation relies on high-resolution spatial discretization of the volume fraction equation, without explicit reconstruction of the phase interface within computational control volumes. One advantage of this approach is that it may be applied on general topology meshes in a straightforward manner. This paper investigates the performance of two different high-resolution discretization schemes used for the solution of the volume fraction equation on three-dimensional unstructured meshes. The schemes are used to obtain results for several

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Xu, Yufeng, and Om P. Agrawal. "Numerical Solutions of Generalized Oscillator Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12705.

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Harmonic oscillators play a fundamental role in many areas of science and engineering, such as classical mechanics, electronics, quantum physics, and others. As a result, harmonic oscillators have been studied extensively. Classical harmonic oscillators are defined using integer order derivatives. In recent years, fractional derivatives have been used to model the behaviors of damped systems more accurately. In this paper, we use three operators called K-, A- and B-operators to define the equation of motion of an oscillator. In contrast to fractional integral and derivative operators which use

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Gadallah, Mohamed H. "Tolerance Optimization: A Decomposition Scheme, Variance Reduction and Fractional Approximation." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/ied-21222.

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Abstract Development of involved optimization algorithms is not an easy task for several reasons: First, every analyst is interested in a specific problem; Second, the capabilities of these methods may not be fully understood a priori; Third, coding of multi-purpose and more involved algorithms is not an easy job. In this paper, the optimization problem employing the near to global optimum algorithm is studied (Gadallah, M.H., 2000). The focus is to exploit 2 ideas: First, the algorithm can be modified to act as a variance reduction technique; Second, the algorithm can be modified to tackle th

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Chao, Fei, Jianqiang Shan, Junli Gou, Pan Wu, and Li Ge. "Assessment of Time and Space High-Order Schemes for Two-Fluid Seven-Equation Two-Pressure Model Using the Reversed Water Faucet Problem." In 2018 26th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icone26-81942.

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The Ransom water faucet problem has become one of the most important benchmark tests to study two-fluid/phase flow because it exists an analytical discontinuous solution. The water faucet problem is a gravity-driven wave problem and its analytical solution is derived from the liquid free fall motion. In this paper, the opposite gravity-driven wave problem named the reversed water faucet problem where the liquid admits a rising motion with reduced speed driven by gravity is studied. With assumptions of decoupled phasic pressures, approximate incompressible flow, no liquid pressure gradient, no

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Duarte, Fernando B. M., and J. A. Tenreiro Machado. "Fractional Order Dynamics in the Trajectory Planning of Redundant and Hyper-Redundant Manipulators." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48383.

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Redundant manipulators have some advantages when compared with classical arms because they allow the trajectory optimization, both on the free space and on the presence of obstacles, and the resolution of singularities. For this type of arms the proposed kinematic control algorithms adopt generalized inverse matrices but, in general, the corresponding trajectory planning schemes show important limitations. Motivated by these problems this paper studies the pseudoinverse-based trajectory planning algorithms, using the theory of fractional calculus.

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Agrawal, Om P., Md Mehedi Hasan, and X. W. Tangpong. "A Numerical Scheme for a Class of Parametric Problem of Fractional Variational Calculus." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48768.

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Fractional derivatives (FDs) or derivatives of arbitrary order have been used in many applications, and it is envisioned that in future they will appear in many functional minimization problems of practical interest. Since fractional derivatives have such property as being non-local, it can be extremely challenging to find analytical solutions for fractional parametric optimization problems, and in many cases, analytical solutions may not exist. Therefore, it is of great importance to develop numerical methods for such problems. This paper presents a numerical scheme for a linear functional mi

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Leonov, A. A., and V. V. Chudanov. "A Discrete Equation Method for Two-Dimensional Calculations of Two-Phase Compressible Mixtures." In 17th International Conference on Nuclear Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/icone17-75586.

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At present time there are different numerical schemes to solve the hyperbolic equations system for two-phase mixture. Those schemes, mainly, rely on a second order Godunov-type scheme (Godunov, 1969), with approximate Riemann solver for the resolution of conservation equations, and set of nonconservative equations. In this paper we applied the Discrete Equation Method (DEM) processed in Saurel & Abgrall (2003) for two-phase compressible mixtures calculation using exact Riemann solver (Leonov & Chudanov, 2008). Thanks to a deeper analysis of the model, a class of schemes, those are able

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