Results 1 to 10 of about 12,358 (240)
General Fractional Vector Calculus [PDF]
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
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General Fractional Calculus: Multi-Kernel Approach [PDF]
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
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General Fractional Calculus in Multi-Dimensional Space: Riesz Form
Mathematics, 2023 An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949.
Vasily E. Tarasov
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Scale-Invariant General Fractional Calculus: Mellin Convolution Operators
Fractal and Fractional, 2023 General fractional calculus (GFC) of operators that is defined through the Mellin convolution instead of Laplace convolution is proposed. This calculus of Mellin convolution operators can be considered as an analogue of the Luchko GFC for the Laplace ...
Vasily E. Tarasov
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General Fractional Integrals and Derivatives with the Sonine Kernels [PDF]
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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Open Physics, 2023 A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established.
Shiri Babak +2 more
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The General Fractional Integrals and Derivatives on a Finite Interval
Mathematics, 2023 The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
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On the Existence and Stability of a Neutral Stochastic Fractional Differential System
Fractal and Fractional, 2022 The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system.
Manzoor Ahmad +4 more
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CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS
Journal of Fundamental Mathematics and Applications (JFMA). This paper discusses the theory of derivatives and integrals in the form of fractions with a particular order initiated by Lioville. Specifically, regarding the correlation between fractional derivatives and integrals, by examining definitions ...
Khairunnisa Fadhilla Ramdhania +4 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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