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Relevant bibliographies by topics / Grünwald letnikov fractional derivative

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Academic literature on the topic 'Grünwald letnikov fractional derivative'

Author: Grafiati

Published: 5 September 2021

Last updated: 26 January 2023

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Journal articles on the topic "Grünwald letnikov fractional derivative"

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Salinas, Matías, Rodrigo Salas, Diego Mellado, Antonio Glaría, and Carolina Saavedra. "A Computational Fractional Signal Derivative Method." Modelling and Simulation in Engineering 2018 (August 1, 2018): 1–10. http://dx.doi.org/10.1155/2018/7280306.

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We propose an efficient computational method to obtain the fractional derivative of a digital signal. The proposal consists of a new interpretation of the Grünwald–Letnikov differintegral operator where we have introduced a finite Cauchy convolution with the Grünwald–Letnikov dynamic kernel. The method can be applied to any signal without knowing its analytical form. In the experiments, we have compared the proposed Grünwald–Letnikov computational fractional derivative method with the Riemman–Louville fractional derivative approach for two well-known functions. The simulations exhibit similar

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Hu, Shaoxiang, та Ping Liang. "Theory Analysis of Left-Handed Grünwald-Letnikov Formula with0<α<1to Detect and Locate Singularities". Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/157542.

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We study fractional-order derivatives of left-handed Grünwald-Letnikov formula with0<α<1to detect and locate singularities in theory. The widely used four types of ideal singularities are analyzed by deducing their fractional derivative formula. The local extrema of fractional derivatives are used to locate the singularities. Theory analysis indicates that fractional-order derivatives of left-handed Grünwald-Letnikov formula with0<α<1can detect and locate four types of ideal singularities correctly, which shows better performance than classical 1-order derivatives in theory.

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Tarasov, Vasily E. "Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach." International Journal of Statistical Mechanics 2014 (December 8, 2014): 1–7. http://dx.doi.org/10.1155/2014/873529.

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Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letn

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Zeng, Min-Li, and Guo-Feng Zhang. "A Banded Preconditioning Iteration Method for Time-Space Fractional Advection-Diffusion Equations." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/6961296.

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In this paper, we concentrate on the efficient solvers for the time-space fractional advection-diffusion equations. Firstly, the implicit finite difference schemes with the shifted Grünwald-Letnikov approximations for spatial fractional derivative and unshifted Grünwald-Letnikov approximations for time fractional derivative are employed to discretize time-space fractional advection-diffusion equations. The discretization results in a series of large dense linear systems. Then, a banded preconditioner is proposed and some theoretical properties for the preconditioning matrix are studied. Numeri

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Jacobs, B. A. "A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme." Abstract and Applied Analysis 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/952057.

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A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.

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Gogoi, Bikash, Utpal Kumar Saha, Bipan Hazarika, Delfim F. M. Torres, and Hijaz Ahmad. "Nabla Fractional Derivative and Fractional Integral on Time Scales." Axioms 10, no. 4 (2021): 317. http://dx.doi.org/10.3390/axioms10040317.

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In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann–Liouville sense. We also introduce the nabla fractional derivative in Grünwald–Letnikov sense. Some of the basic properties and theorems related to nabla fractional calculus are discussed.

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Zeb, Anwar, Vedat Suat Erturk, Umar Khan, Gul Zaman, and Shaher Momani. "An approach for approximate solution of fractional-order smoking model with relapse class." International Journal of Biomathematics 11, no. 06 (2018): 1850077. http://dx.doi.org/10.1142/s1793524518500778.

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In this paper, we develop a fractional-order smoking model by considering relapse class. First, we formulate the model and find the unique positive solution for the proposed model. Then we apply the Grünwald–Letnikov approximation in the place of maintaining a general quadrature formula approach to the Riemann–Liouville integral definition of the fractional derivative. Building on this foundation avoids the need for domain transformations, contour integration or involved theory to compute accurate approximate solutions of fractional-order giving up smoking model. A comparative study between Gr

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Billur İskender Eroğlu, Beyza, Derya Avcı, and Necati Özdemir. "Constrained Optimal Control of A Fractionally Damped Elastic Beam." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 3-4 (2020): 389–95. http://dx.doi.org/10.1515/ijnsns-2018-0393.

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AbstractThis work presents the constrained optimal control of a fractionally damped elastic beam in which the damping characteristic is described with the Caputo fractional derivative of order 1/2. To achieve the optimal control that involves energy optimal control index with fixed endpoints, the fractionally damped elastic beam problem is first converted to a state space form of order 1/2 by using a change of coordinates. Then, the state and the costate equations are set in terms of Hamiltonian formalism and the constrained control law is acquired from Pontryagin Principle. The numerical solu

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Ozturk, Okkes, and Resat Yilmazer. "An Application of the Sonine–Letnikov Fractional Derivative for the Radial Schrödinger Equation." Fractal and Fractional 3, no. 2 (2019): 16. http://dx.doi.org/10.3390/fractalfract3020016.

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The Sonine–Letnikov fractional derivative provides the generalized Leibniz rule and, some singular differential equations with integer order can be transformed into the fractional differential equations. The solutions of these equations obtained by some transformations have the fractional forms, and these forms can be obtained as the explicit solutions of these singular equations by using the fractional calculus definitions of Riemann–Liouville, Grünwald–Letnikov, Caputo, etc. Explicit solutions of the Schrödinger equation have an important position in quantum mechanics due to the fact that th

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Kern, Peter, Svenja Lage, and Mark M. Meerschaert. "Semi-fractional diffusion equations." Fractional Calculus and Applied Analysis 22, no. 2 (2019): 326–57. http://dx.doi.org/10.1515/fca-2019-0021.

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Abstract It is well known that certain fractional diffusion equations can be solved by the densities of stable Lévy motions. In this paper we use the classical semigroup approach for Lévy processes to define semi-fractional derivatives, which allows us to generalize this statement to semistable Lévy processes. A Fourier series approach for the periodic part of the corresponding Lévy exponents enables us to represent semi-fractional derivatives by a Grünwald-Letnikov type formula. We use this formula to calculate semi-fractional derivatives and solutions to semi-fractional diffusion equations n

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Dissertations / Theses on the topic "Grünwald letnikov fractional derivative"

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Kadlčík, Libor. "Efektivní použití obvodů zlomkového řádu v integrované technice." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2020. http://www.nusl.cz/ntk/nusl-432494.

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Integrace a derivace jsou obvykle známy pro celočíselný řád (tj. první, druhý, atd.). Existuje ale zobecnění pro zlomkové (neceločíselné) řády, které lze implementovat pomocí elektronických obvodů zlomkového řádu (případně provést jejich aproximaci) a které poskytuje nový stupeň volnosti pro návrh elektronických obvodů. Obvody zlomkového řádu jsou obvykle aproximovány diskrétními součástkami pomocí RC struktur s velkými rozsahy odporů a kapacit, a tím se jeví nepraktické pro použití v integrovaných obvodech. Tato práce prezentuje implementaci obvodů zlomkového řádu v integerovaných obvodech a

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Hejazi, Hala Ahmad. "Finite volume methods for simulating anomalous transport." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/81751/1/Hala%20Ahmad_Hejazi_Thesis.pdf.

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In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

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Yang, Qianqian. "Novel analytical and numerical methods for solving fractional dynamical systems." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/35750/1/Qianqian_Yang_Thesis.pdf.

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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional deri

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Paiva, Maria Inês Patrício. "Métodos numéricos para modelos de preços de opções baseados em processos de Lévy." Master's thesis, 2021. http://hdl.handle.net/10316/95508.

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Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia<br>O modelo de Black-Scholes foi um dos primeiros modelos de preços de opções europeias a ser aceite. Ainda hoje, este modelo desempenha um papel fundamental na previsão dos preços de uma opção, devido à facilidade que existe na sua implementação e ao facto da sua fórmula só depender de um único parâmetro não observável. No entanto, também apresenta algumas limitações, por causa de suposições estritas ou pouco realistas que lhe estão subjacentes. Daí que, foram desenvolvidos outros modelos que contornassem e

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Book chapters on the topic "Grünwald letnikov fractional derivative"

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Latawiec, Krzysztof J., Rafał Stanisławski, Marian Łukaniszyn, Marek Rydel, and Bogusław R. Szkuta. "Grünwald-Letnikov-Laguerre Modeling of Discrete-Time Noncommensurate Fractional-Order State Space LTI MIMO Systems." In Lecture Notes in Electrical Engineering. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78458-8_7.

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Matusiak, Mariusz. "Fast Evaluation of Grünwald-Letnikov Variable Fractional-Order Differentiation and Integration Based on the FFT Convolution." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50936-1_74.

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Kozioł, Kamil, and Rafał Stanisławski. "Selected Implementation Issues in Computation of the Grünwald-Letnikov Fractional-Order Difference by Means of Embedded System." In Lecture Notes in Electrical Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17344-9_7.

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Fujioka, J., M. Velasco, A. Ramírez, and A. Espinosa-Cerón. "Fractional Noether´s Theorem and Fractional Optical Solitons with Ortigueira´s and Grünwald-Letnikov´s Derivatives." In Recent Advances in Mathematical Research and Computer Science Vol. 9. Book Publisher International (a part of SCIENCEDOMAIN International), 2022. http://dx.doi.org/10.9734/bpi/ramrcs/v9/15648d.

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Khettab, Khatir, and Yassine Bensafia. "An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination." 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.ch004.

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This chapter presents a fractional adaptive interval type-2 fuzzy logic control strategy based on active fractional sliding mode controller (FAIT2FSMC) to synchronize tow chaotic fractional-order systems. The interval type-2 fuzzy logic systems (IT2FLS) are used to approximate the plant dynamics represented by unknown functions of the system, and the IT2F adaptation law adjusts the consequent parameters of the rules based on a Lyapunov synthesis approach. One of the main contributions in this work is the use of an IT2F and an adaptive fractional order PIλ control law to eliminate the chattering action in the control signal. Based on fractional order Lyapunov stability criterion, stability analysis is performed for the proposed method for an acceptable synchronization error level. The performance of the proposed scheme is demonstrated through the synchronization of two different fractional order chaotic gyro systems. Simulations are implemented using a numerical method based on Grünwald-Letnikov approach to solve the fractional differential equations.

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Ganga, M., N. Janakiraman, Arun Kumar Sivaraman, Rajiv Vincent, A. Muralidhar, and Priya Ravindran. "An Effective Denoising and Enhancement Strategy for Medical Image Using Rl-Gl-Caputo Method." In Advances in Parallel Computing. IOS Press, 2021. http://dx.doi.org/10.3233/apc210074.

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At present, fractional differential is the effective mathematical approach which deals with the factual problems. This projected technique employs the fractional derivatives definitions Riemann-Liouville (R-L), Grunwald-Letnikov (G-L) and the caputo technique for denoising medical image. The presented method based on fractional derivative which in turn improves the quality of image. The input image is processed on integer order method such as pre-processing operation, image conversion and noise image. The fractional differential mask method is to be applied with the help of Riemann Liouville, and Caputo algorithm. After denoising the medical image enhanced using Anisotropic diffusion process and the result is analyzed to finally get denoised and predicted image.

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Conference papers on the topic "Grünwald letnikov fractional derivative"

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Mozyrska, Dorota, and Piotr Ostalczyk. "Variable-, fractional-order Grünwald-Letnikov backward difference selected properties." In 2016 39th International Conference on Telecommunications and Signal Processing (TSP). IEEE, 2016. http://dx.doi.org/10.1109/tsp.2016.7760959.

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Wei, Yiheng, YangQuan Chen, Peter W. Tse, and Songsong Cheng. "Analytical and numerical representations for discrete Grünwald–Letnikov fractional calculus." In 2020 Chinese Automation Congress (CAC). IEEE, 2020. http://dx.doi.org/10.1109/cac51589.2020.9327090.

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Ortigueira, Manuel D., and Juan J. Trujillo. "On a Unified Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47317.

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A new fractional derivative of complex Gru¨wald-Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Gru¨wald-Letnikov and other fractional derivatives well known. Several properties of such generalized operator are presented.

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Oziablo, Piotr, Dorota Mozyrska, and Malgorzata Wyrwas. "A digital PID controller based on Grünwald-Letnikov fractional-, variable-order operator." In 2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE, 2019. http://dx.doi.org/10.1109/mmar.2019.8864688.

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Stanislawski, Rafal, Krzysztof J. Latawiec, Marian Lukaniszyn, Wojciech Czuczwara, and Ryszard Kopka. "Modeling and identification of fractional first-order systems with Laguerre-Grünwald-Letnikov fractional-order differences." In 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE, 2016. http://dx.doi.org/10.1109/mmar.2016.7575128.

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The, Anh Pham, Piotr Jurgás, Michał Niezabitowski, and Stefan Siegmund. "Variation of constant formulas of linear autonomous Grünwald-Letnikov-type fractional difference equations." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114549.

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Biswas, Raj Kumar, and Siddhartha Sen. "Fractional Optimal Control Within Caputo’s Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48045.

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A general formulation and solution of fractional optimal control problems (FOCPs) in terms of Caputo fractional derivatives (CFDs) of arbitrary order have been considered in this paper. The performance index (PI) of a FOCP is considered as a function of both the state and control. The dynamic constraint is expressed by a fractional differential equation (FDE) of arbitrary order. A general pseudo-state-space representation of the FDE is presented and based on that, FOCP has been developed. A numerical technique based on Gru¨nwald-Letnikov (G-L) approximation of the FDs is used for solving the r

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Clemente-Lopez, D., J. M. Munoz-Pacheco, O. G. Felix-Beltran, and C. Volos. "Efficient Computation of the Grünwald-Letnikov Method for ARM-Based Implementations of Fractional-Order Chaotic Systems." In 2019 8th International Conference on Modern Circuits and Systems Technologies (MOCAST). IEEE, 2019. http://dx.doi.org/10.1109/mocast.2019.8742063.

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Ortigueira, Manuel D., and Juan J. Trujillo. "Generalized GL Fractional Derivative and Its Laplace and Fourier Transform." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87238.

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It is well known the difficulties that the Riesz fractional derivative present, as the spatial fractional derivative involved in many models of the dynamics of anomalous processes. The generalized Gru¨nwal-Letnikov fractional derivative is analysed in this paper. Its Laplace and Fourier Transforms are computed and some current results criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

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Zhang, Guimei, Yangang Zhu, Jianxin Liu, and YangQuan Chen. "Image Segmentation Based on Fractional Differentiation and RSF Model." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67110.

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Intensity inhomogeneity or weak texture region image segmentation plays an important role in computer vision and image processing. RSF (Region-Scalable Fitting) active contour model has been proved to be an effective method to segment intensity inhomogeneity. However RSF model is sensitive to the initial location of evolution curve , it tends to fall into local optimal. Aiming at the problem, this paper proposed a new method for image segmentation based on fractional differentiation and RSF model. The proposed method adds the global Grünwald-Letnikov fractional gradient into the RSF model. Thu

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