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
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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
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
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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
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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
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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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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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Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets [PDF]
, 2009 We prove a Calder\'on reproducing formula for the Dunkl continuous wavelet transform on $\mathbb{R}$.
Mourou, Mohamed Ali
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Variable-order fractional calculus: A change of perspective [PDF]
, 2021 Several approaches to the formulation of a fractional theory of calculus of “variable order” have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an alternative view on
Garrappa R., Giusti A., Mainardi F.
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Trends, directions for further research, and some open problems of fractional calculus [PDF]
, 2021 The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at ...
Diethelm, Kai +4 more
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