Results 1 to 10 of about 879 (146)
Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations [PDF]
Journal of Advanced Research, 2023 Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari +2 more
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On Fractional Orthonormal Polynomials of a Discrete Variable [PDF]
Discrete Dynamics in Nature and Society, 2015 A fractional analogue of classical Gram or discrete Chebyshev polynomials is introduced. Basic properties as well as their relation with the fractional analogue of Legendre polynomials are presented.
I. Area +3 more
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Results in Physics, 2023 In this study, multi-term time fractional 2D telegraph type equations, as a new category of fractional differential equations, are introduced. The orthonormal Chelyshkov polynomials are used as basis functions to generate a collocation method for such ...
M.H. Heydari, M. Razzaghi, Sh. Karami
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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials
Mathematics, 2020 In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator,
Juan F. Mañas-Mañas +2 more
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A hybrid approach for piecewise fractional reaction–diffusion equations
Results in Physics, 2023 In this paper, the Caputo and Atangana–Baleanu fractional derivatives are handled to introduce a type of piecewise fractional derivative. More precisely, a linear combination of the Caputo and Atangana–Baleanu fractional derivatives are considered in ...
M.H. Heydari, Sh. Zhagharian
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Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials [PDF]
Journal of the Optical Society of America A, 2018 The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle ...
Cosmas Mafusire, Tjaart P. J. Krüger
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ESTIMATES FOR SOBOLEV-ORTHONORMAL FUNCTIONS AND GENERATED BY LAGUERRE FUNCTIONS
Проблемы анализа, 2021 In this paper, we consider the system of functions λ^α_(r,n(x)) (n = 0, 1, . . .), α > −1, r ∈ N, orthonormal with respect to a Sobolev-type inner product and generated by the system of Laguerre functions.
R. M. Gadzhimirzaev
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A numerical method for distributed-order time fractional 2D Sobolev equation
Results in Physics, 2023 In this work, the distributed-order time fractional 2D Sobolev equation is introduced. The orthonormal Bernoulli polynomials, as a renowned family of basis functions, are employed to solve this problem.
M.H. Heydari, S. Rashid, F. Jarad
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Advances in Difference Equations, 2021 This paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order fractional version of the Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family of basis functions, are
M. H. Heydari, A. Atangana
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