General Fractional Integrals and Derivatives with the Sonine Kernels
Mathematics, 2021 In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
exaly +6 more sources
On generalized fractional differential equation with Sonine kernel on a function space
Partial Differential Equations in Applied MathematicsSonine kernel is a special type of the general kernels, satisfying some integrability and monotonicity conditions and properties. Sonine kernels generate some convolution polynomials (power functions) used in the construction of the general fractional ...
McSylvester Ejighikeme Omaba
exaly +4 more sources
Stability of Delay Hopfield Neural Networks with Generalized Riemann-Liouville Type Fractional Derivative. [PDF]
Entropy (Basel), 2023 The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann–Liouville fractional derivative (GRLFD) with an exponential ...
Agarwal RP, Hristova S.
europepmc +2 more sources
A Rigorous Analysis of Integro-Differential Operators with Non-Singular Kernels
Fractal and Fractional, 2023 Integro-differential operators with non-singular kernels have been much discussed among fractional calculus researchers. We present a mathematical study to clearly establish the rigorous foundations of this topic.
Arran Fernandez, Mohammed Al-Refai
doaj +2 more sources
Sonine Transform Associated to the Dunkl Kernel on the Real Line [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 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 $\mathbb{R}$. Next, we introduce complex powers of the Dunkl Laplacian $Δ_α$ and establish inversion formulas for the Dunkl Sonine operator $S_{α,β}$ and its dual ${}^tS_{α,β}$.
Fethi Soltani
core +7 more sources
Extending Sonine kernels to arbitrary dimensions
Banach Journal of Mathematical AnalysisAbstract The theory of general fractional calculus with Sonine kernels has been well developed by Luchko in the one-dimensional case. Inspired by recent work on Mikusiński’s operational calculus for fractional partial differential operators, we construct a multi-dimensional version of the theory of Sonine kernels, solving a recognised open ...
Arran Fernández
exaly +2 more sources
Operators associated with soft and hard spectral edges from unitary ensembles. [PDF]
, 2008 Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as
Blower, Gordon
core +5 more sources
Nonexistence of Finite-Time Stable Equilibria in a Class of Nonlinear Integral Equations
Fractal and Fractional, 2023 This brief report studies conditions to ensure the nonexistence of finite-time stable equilibria in a class of systems that are described by means of nonlinear integral equations, whose kernels are part of some Sonine kernel pairs.
Aldo Jonathan Muñoz-Vázquez +2 more
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source