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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An equivalent formulation of Sonine condition [PDF]
Applied Mathematics LettersSonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations. This work proposes a SC with a more general form (denoted by gSC), which is more convenient than SC to accommodate complex kernels and equations.
Xiangcheng Zheng
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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
doaj +2 more sources
Is Comprehension in Comics More Effective Than in Traditional Texts in Skilled Adult Readers? An Eye Movement-Based Study. [PDF]
Cogn SciAbstract Reading comprehension has been mostly studied using traditional texts and very little is known about reading comprehension in comics. We wanted to find out whether comics could enhance comprehension processes, compared to traditional text and what cognitive processes might be involved in this effect.
Rasamimanana M +4 more
europepmc +2 more sources
Fractal and FractionalTraditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address
Yajun Yin, Zelin Liu
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Some notes on Sonine–Gegenbauer integrals [PDF]
Integral Transforms and Special Functions, 2019 Grandits P.
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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
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 +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