Results 1 to 10 of about 11,408,380 (251)
Growth Equation of the General Fractional Calculus
Mathematics, 2019 We consider the Cauchy problem ( D ( k ) u ) ( t ) = λ u ( t ) , u ( 0 ) = 1 , where D ( k ) is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory 71 (2011),
Anatoly N. Kochubei, Yuri Kondratiev
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Mathematics, 2023 Significant progress has been made in incorporating fractional calculus into the projection and lag synchronization of complex networks. However, real-world networks are highly complex, making the fractional derivative used in complex dynamics more ...
Zhenduo Sun +2 more
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On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
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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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations
Abstract and Applied Analysis, 2011 This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the ...
Jan Čermák +2 more
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Analysis of the family of integral equation involving incomplete types of I and Ī-functions
Applied Mathematics in Science and Engineering, 2023 The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete $ \bar {I} $ -function (I $ \bar {I} $ F) in its kernel.
Sanjay Bhatter +5 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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On certain fractional calculus operators involving generalized Mittag-Leffler function [PDF]
Sahand Communications in Mathematical Analysis, 2016 The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25].
Dinesh Kumar
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Journal of Advanced Engineering and Computation, 2021 This survey-cum-expository review article is motivated essentially by the widespread usages of the operators of fractional calculus (that is, fractional-order integrals and fractional-order derivatives) in the modeling and analysis of a remarkably large ...
Hari Mohan Srivastava
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Nonlinear Analysis, 2022 General fractional calculus is popular recently. Fractional uncertain differential equations (FUDEs) with general memory effects are proposed in this paper.
Cheng Luo, Guo-Cheng Wu, Lan-Lan Huang
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