Fractional-order general Lagrange scaling functions and their applications

Sabermahani, Sedigheh; Ordokhani, Yadollah; Yousefi, S. A.

doi:10.1007/s10543-019-00769-0

Cited by 27 publications

(15 citation statements)

References 33 publications

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“…The generalized Laguerre polynomials (GLPs), also known as associated Laguerre polynomials [29], are…”

Section: Generalized Laguerre Polynomialsmentioning

confidence: 99%

“…The new fractional-order orthogonal moments [15] effectively improve the performance of orthogonal moments in image analysis, and can also improve the quaternion color-image moments. The basis function of fractional-order orthogonal moments comprises a set of fractional-order (or real-order) orthogonal polynomials rather than traditional integer-order polynomials [16,17].…”

Section: Introductionmentioning

confidence: 99%

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Novel Color Orthogonal Moments-Based Image Representation and Recognition

He¹,

Li²,

Yang³

et al. 2020

Preprint

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Inspired by quaternion algebra and the idea of fractional-order transformation, we propose a new set of quaternion fractional-order generalized Laguerre orthogonal moments (QFr-GLMs) based on fractional-order generalized Laguerre polynomials. Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.

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“…The generalized Laguerre polynomials (GLPs), also known as associated Laguerre polynomials [29], are…”

Section: Generalized Laguerre Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Novel Color Orthogonal Moments-Based Image Representation and Recognition

He¹,

Li²,

Yang³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Sabermahani et al (2018) proposed a set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Sabermahani et al (2020a) introduced a formulation for fractional-order general Lagrange scaling functions and employed these functions for solving fractional differential equations. Sabermahani et al (2020b) used hybrid functions of block-pulse and fractional-order Fibonacci polynomials for obtaining the approximate solution of fractional delay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

et al. 2020

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This paper addresses the application of generalized polynomials for solving nonlinear systems of fractional-order partial differential equations with initial conditions. First, the solutions are expanded by means of generalized polynomials through an operational matrix. The unknown free coefficients and control parameters of the expansion with generalized polynomials are evaluated by means of an optimization process relating the nonlinear systems of fractionalorder partial differential equations with the initial conditions. Then, the Lagrange multipliers are adopted for converting the problem into a system of algebraic equations. The convergence of the proposed method is analyzed. Several prototype problems show the applicability of the algorithm. The approximations obtained by other techniques are also tested confirming the high accuracy and computational efficiency of the proposed approach.

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“…Several numerical methods to solve the delay differential equations has been presented such as hybrid-Chebyshev polynomials, 14 fractional-order general Lagrange scaling functions, 15 hybrid-Legendre polynomials, hybrid-Taylor polynomials, 16 and fractional-order hybrid functions. 17 Another important class of delay problems is optimal control problems that are used to model many of the phenomena, which we mention here.…”

Section: Introductionmentioning

confidence: 99%

“…Several numerical methods to solve the delay differential equations has been presented such as hybrid‐Chebyshev polynomials, fractional‐order general Lagrange scaling functions, hybrid‐Legendre polynomials, hybrid‐Taylor polynomials, and fractional‐order hybrid functions …”

Section: Introductionmentioning

confidence: 99%

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

Sabermahani

Ordokhani

Yousefi

2019

Optim Control Appl Methods

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Summary In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique.

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Fractional-order general Lagrange scaling functions and their applications

Cited by 27 publications

References 33 publications

Novel Color Orthogonal Moments-Based Image Representation and Recognition

Novel Color Orthogonal Moments-Based Image Representation and Recognition

Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

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