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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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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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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Alexandria Engineering Journal, 2023 In this paper, the distributed-order time fractional diffusion equation is introduced and studied. The Caputo fractional derivative is utilized to define this distributed-order fractional derivative.
M.H. Heydari, M. Hosseininia, D. Baleanu
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Recovery of a distributed order fractional derivative in an unknown medium
Communications in Mathematical Sciences, 2023 In this work, we study an inverse problem of recovering information about the weight in distributed-order time-fractional diffusion from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of the medium, we prove that the one-point observation can uniquely determine the support bound of the weight.
Jin, B, Kian, Y
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Fractional diffusion equation with distributed-order Caputo derivative [PDF]
Journal of Integral Equations and Applications, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kubica, Adam, Ryszewska, Katarzyna
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