Stability of Delay Hopfield Neural Networks with Generalized Riemann–Liouville Type Fractional Derivative [PDF]
Entropy, 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 ...
Ravi P. Agarwal, Snezhana Hristova
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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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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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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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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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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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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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Kovacs-like memory effect in athermal systems: linear response analysis [PDF]
, 2017 We analyse the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically relevant moments ...
Plata, Carlos A., Prados, Antonio
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Statistical properties of inelastic Lorentz gas [PDF]
, 2001 The inelastic Lorentz gas in cooling states is studied. It is found that the inelastic Lorentz gas is localized and that the mean square displacement of the inelastic Lorentz gas obeys a power of a logarithmic function of time.
CRC, McElwee G., OECD
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