Results 11 to 20 of about 2,538,078 (99)
Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications
Mathematics, 2021 In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero.
Yuri Luchko
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Mathematics, 2022 In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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Simplified Mixing Rules for Calculating Transport Coefficients of High‐Temperature Air
International Journal of Aerospace Engineering, Volume 2023, Issue 1, 2023., 2023 The transport process of high‐temperature air is vital in aerospace fields and has attracted increased attention in recent years. In this paper, an adequate study of factors affecting transport coefficients for high‐temperature air is conducted. The results of a different‐species model at different pressures and temperatures show that the 9‐species air
Zhe Wang +3 more
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Homotopy operators for the variational bicomplex, representations of the Euler-Lagrange complex, and the Helmholtz-Sonin conditions [PDF]
Lobachevskii Journal of Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Crampin, Michael, Saunders, David J
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Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets [PDF]
, 2009 We prove a Calderón reproducing formula for the Dunkl continuous wavelet transform on R.
Mohamed Ali Mourou
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The General Fractional Derivative and Related Fractional Differential Equations
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
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Generalising the fractional calculus with Sonine kernels via conjugations
, 2023 Many different types of fractional calculus are defined by various kernel functions within the general class of Sonine-type kernels, while many others are given by conjugating the usual fractional calculus with invertible linear operators, such as ...
Arran Fernandez +3 more
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Sonine Transform Associated to the Dunkl Kernel on the Real Line [PDF]
, 2008 We consider the Dunkl intertwining operator V_α and its dual ^tV_α, we define and study the Dunkl Sonine operator and its dual on R. Next, we introduce complex powers of the Dunkl Laplacian Δ_α and establish inversion formulas for the Dunkl Sonine ...
Fethi Soltani
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Journal of Applied Mathematics, Volume 2016, Issue 1, 2016., 2016 We prove existence and uniqueness of the solution of the problem with initial and Maxwell‐Auzhan boundary conditions for nonstationary nonlinear one‐dimensional Boltzmann’s six‐moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary
A. Sakabekov +2 more
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A characterization of the four Chebyshev orthogonal families
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 13, Page 2071-2079, 2005., 2005 We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences.
E. Berriochoa +2 more
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