Vibration Systems with Fractional-Order and Distributed-Order Derivatives Characterizing Viscoinertia [PDF]
Fractal and Fractional, 2021 We considered forced harmonic vibration systems with the Liouville–Weyl fractional derivative where the order is between 1 and 2 and with a distributed-order derivative where the Liouville–Weyl fractional derivatives are integrated on the interval [1, 2]
Jun-Sheng Duan, Di-Chen Hu
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Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels [PDF]
Mathematics, 2021 In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator.
Fátima Cruz +2 more
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Computational Solutions of Distributed Order Reaction-Diffusion Systems Associated with Riemann-Liouville Derivatives [PDF]
Axioms, 2015 This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as ...
Ram K. Saxena +2 more
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Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative [PDF]
Applied Sciences, 2021 A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel.
Nehad Ali Shah +4 more
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Open Physics, 2017 We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative.
Duan Jun-Sheng +2 more
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Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo–Fabrizio fractional derivative [PDF]
Advances in Difference Equations, 2020 We consider distributed-order partial differential equations with time fractional derivative proposed by Caputo and Fabrizio in a one-dimensional space. Two finite difference schemes are established via Grünwald formula.
Haili Qiao, Zhengguang Liu, Aijie Cheng
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The Kernel of the Distributed Order Fractional Derivatives with an Application to Complex Materials
Fractal and Fractional, 2017 The extension of the fractional order derivative to the distributed order fractional derivative (DOFD) is somewhat simple from a formal point of view, but it does not yet have a simple, obvious analytic form that allows its fast numerical calculation ...
Michele Caputo, Mauro Fabrizio
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Quasi-Projective Synchronization of Distributed-Order Recurrent Neural Networks
Fractal and Fractional, 2021 In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential ...
Xiao Liu +3 more
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On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory
Fractal and Fractional, 2023 A novel two-compartment model for drug release was formulated. The general fractional derivatives of a specific type and distributed order were used in the formulation. Earlier used models in pharmacokinetics with fractional derivatives follow as special
Vesna Miskovic-Stankovic +1 more
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Results in Physics, 2023 This work deals with the distributed-order time fractional nonlinear diffusion-wave equations. These equations are generated by replacing the first- and second-order time derivative terms with the distributed-order fractional derivative terms.
M.H. Heydari, S. Rashid, Yu-Ming Chu
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