Results 51 to 60 of about 374,024 (252)
Advances in Mathematical Physics, 2013 We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the ...
Mohsen Alipour, Dumitru Baleanu
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Mathematical Model of Fractional Duffing Oscillator with Variable Memory
Mathematics, 2020 The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional
Valentine Kim, Roman Parovik
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Fractal and Fractional, 2022 First, we show the equivalence of two definitions of the left Riemann–Liouville fractional integral on time scales. Then, we establish and characterize fractional Sobolev space with the help of the notion of left Riemann–Liouville fractional derivative ...
Xing Hu, Yongkun Li
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Can we split fractional derivative while analyzing fractional differential equations? [PDF]
Communications in Nonlinear Science and Numerical Simulation 76
(2019): 12-24, 2019 Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders $\alpha$ and $\beta$ in ${}_0^{C}\mathrm{D}_t^\alpha {}_0^{C}\mathrm{D}_t^\beta$ to produce the fractional derivative ${}
arxiv +1 more source
Fractional generalizations of filtering problems and their associated fractional Zakai equations [PDF]
, 2014 In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering
Daum, Frederick +2 more
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Analysis and Modeling of Fractional-Order Buck Converter Based on Riemann-Liouville Derivative
IEEE Access, 2019 In previous studies, researchers used the fractional definition of Caputo to study fractional-order power converter. However, it is found that the model based on Caputo fractional definition is inconsistent with the actual situation.
Zhihao Wei, Bo Zhang, Yanwei Jiang
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Weyl Quantization of Fractional Derivatives
, 2009 The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives.
Kilbas A. A. +8 more
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Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivative [PDF]
Applied Numerical Mathematics, 2019 32 pages, 2 ...
Daxin Nie, Jing Sun, Weihua Deng
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A New Generalized Definition of Fractional Derivative with Non-Singular Kernel
Computation, 2020 This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined.
Khalid Hattaf
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Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy
, 2010 With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations.
Adda +64 more
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