Results 31 to 40 of about 29,097 (308)
Discrete Dynamics in Nature and Society, 2018 This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations ...
Bochao Chen, Li Qin, Fei Xu, Jian Zu
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Applied Mathematics in Science and Engineering, 2023 This study presents an efficient method that is suitable for differential equations, both with integer-order and fractional derivatives. This study examines the construction of solutions of fractional differential equations that are associated with ...
M.O. Aibinu, E. Momoniat
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Neural fractional differential equations
Applied Mathematical ModellingFractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours.
C. Coelho +2 more
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Advances in Difference Equations, 2017 We propose a new method called the fractional reduced differential transform method (FRDTM) to solve nonlinear fractional partial differential equations such as the space-time fractional Burgers equations and the time-fractional Cahn-Allen equation.
Mahmoud S Rawashdeh
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Weak Solutions for Time-Fractional Evolution Equations in Hilbert Spaces
Fractal and Fractional, 2021 Our purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative.
Paola Loreti, Daniela Sforza
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Continuous extensions of numerical methods for Stochastic Fractional Differential Equations
, 2021 We present a technique to provide continuous-time extension of numerical methods solving Stochastic Fractional Differential Equations (SFDEs). The basic idea we follow is closely related to the classic scenario of deterministic collocation methods for ...
Giordano Giuseppe +3 more
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Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2
上海师范大学学报. 自然科学版, 2015 This paper is mainly concerned with the asymptotic stability of the solutions of a class of nonlinear fractional differential equations of order 1 < α < 2 in a weighted Banach space.
GE Fudong, KOU Chunhai
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Fractal and Fractional, 2023 This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation points and derived the ...
Zhongshu Wu +3 more
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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Frontiers in PhysicsThe symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations ...
Mashael M. ALBaidani +2 more
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