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Applications of Distributed-Order Fractional Operators: A Review [PDF]
Entropy, 2021 Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of
Wei Ding +3 more
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General Fractional Calculus Operators of Distributed Order
Axioms, 2023 In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
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Stability Analysis of Distributed Order Fractional Chen System [PDF]
The Scientific World Journal, 2013 We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain.
H. Aminikhah +2 more
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Pontryagin Maximum Principle for Distributed-Order Fractional Systems [PDF]
Mathematics, 2021 We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type.
Faïçal Ndaïrou, Delfim F. M. Torres
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Stability Analysis on Nabla Discrete Distributed-Order Dynamical System
Fractal and Fractional, 2022 This paper addresses the problems of the stability of a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on a proposed generalized definition of discrete integral, some related definitions of nabla discrete distributed-order ...
Xiang Wu +3 more
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Haar wavelet method for solution of distributed order time-fractional differential equations
Alexandria Engineering Journal, 2021 This manuscript is related to compute approximate solutions for a class of fractional distributed order differential equations (FDODEs). The corresponding derivative of fractional order is taken in Caputo sense.
Rohul Amin +5 more
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A generalised distributed‐order Maxwell model [PDF]
Mathematical methods in the applied sciences, 2022 In this work, we present a generalised viscoelastic model using distributed‐order derivatives. The model consists of two distributed‐order elements (distributed springpots) connected in series, as in the Maxwell model.
L. L. Ferrás, M. Morgado, M. Rebelo
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Mathematical Modelling and Analysis, 2022 In this study, an accurate and efficient composite collocation method based on the fractional order Chelyshkov wavelets is proposed for obtaining approximate solution of distributed-order fractional mobile-immobile advection-dispersion equation with ...
Hamidreza Marasi +1 more
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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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Multiscale Nonlocal Elasticity: A Distributed Order Fractional Formulation [PDF]
International Journal of Mechanical Sciences, 2021 This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal multiscale behavior
Wei Ding, Sansit Patnaik, F. Semperlotti
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