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The General Fractional Derivative and Related Fractional Differential Equations [PDF]
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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Fuzzy Generalized Conformable Fractional Derivative [PDF]
Advances in Fuzzy Systems, 2020 We give a new definition of fuzzy fractional derivative called fuzzy conformable fractional derivative. Using this definition, we prove some results and we introduce new definition of generalized fuzzy conformable fractional derivative.
Atimad Harir +2 more
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Electrical Circuits Described by General Fractional Conformable Derivative
Frontiers in Energy Research, 2022 The general fractional conformable derivative (GCD) and its attributes have been described by researchers in the recent times. Compared with other fractional derivative definitions, this derivative presents a generalization of the conformable derivative ...
Omar Kahouli +8 more
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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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Finite element implementation of general triangular mesh for Riesz derivative
Partial Differential Equations in Applied Mathematics, 2021 In this work, we will study a calculation method of variation formula with Riesz fractional derivative. As far as we know, Riesz derivative is a non-local operator including 2ndirections in n−dimension space, which the difficulties for computation of ...
Daopeng Yin, Liquan Mei
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Green’s theorem for generalized fractional derivatives [PDF]
Fractional Calculus and Applied Analysis, 2013 We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case when the generalized operators are reduced to the standard partial fractional derivatives and fractional integrals in
Odzijewicz, T. +2 more
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Journal of Algorithms & Computational Technology, 2023 For scientists conducting research, fractional integral differential equation analysis is crucial. Therefore, in this study, we investigate analysis utilizing a novel method called the fractional decomposition method, which is applicable to fractional ...
Mahmoud S Rawashdeh +2 more
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Alexandria Engineering Journal, 2023 In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the
Shorish Omer Abdulla +2 more
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Generalized Hamilton's principle with fractional derivatives [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t), )$ so that the function $y$ and the order of fractional derivative $ $ are varied in the minimization procedure. We derive stationarity conditions and discuss them through several examples.
Atanacković, Teodor +3 more
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Fractional Sumudu Decomposition Method for Solving PDEs of Fractional Order [PDF]
Journal of Applied and Computational Mechanics, 2021 . In this paper, the fractional Sumudu decomposition method (FSDM) is employed to handle the time-fractional PDEs and system of time-fractional PDEs. The fractional derivative is described in the Caputo sense.
Hassan Kamil Jassim, Habeeb Kadmim
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