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International Journal of Computer Mathematics Volume 95, 2018 - Issue 6-7: Advances on Computational Fractional Partial Differential Equations
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Original Articles

Fractional pseudo-spectral methods for distributed-order fractional PDEs

Ehsan KharazmiDepartment of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA;Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USAView further author information
&
Mohsen ZayernouriDepartment of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA;Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USACorrespondence[email protected]
[email protected]
View further author information
Pages 1340-1361 | Received 15 May 2017, Accepted 11 Sep 2017, Published online: 30 Jan 2018

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Khadijeh Sadri, Kamyar Hosseini, Dumitru Baleanu & Soheil Salahshour. (2022) A high-accuracy Vieta-Fibonacci collocation scheme to solve linear time-fractional telegraph equations. Waves in Random and Complex Media 0:0, pages 1-24.
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Mahmoud A. Zaky & Ahmed S. Hendy. (2021) Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations. International Journal of Computer Mathematics 98:7, pages 1420-1437.
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Jorge L. Suzuki & Mohsen Zayernouri. (2021) A self-singularity-capturing scheme for fractional differential equations. International Journal of Computer Mathematics 98:5, pages 933-960.
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Hao Yu, Boying Wu & Dazhi Zhang. (2020) A Hermite spectral method for fractional convection diffusion equations on unbounded domains. International Journal of Computer Mathematics 97:10, pages 2142-2163.
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M. Ari, R. T. Faal & M. Zayernouri. (2020) Vibrations suppression of fractionally damped plates using multiple optimal dynamic vibration absorbers. International Journal of Computer Mathematics 97:4, pages 851-874.
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T. A. Biala. (2019) Second-order predictor-corrector schemes for nonlinear distributed-order space-fractional differential equations with non-smooth initial data. International Journal of Computer Mathematics 96:9, pages 1861-1878.
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Articles from other publishers (22)

Mohammad Hossein Derakhshan, Hamid Rezaei & Hamid Reza Marasi. (2023) An efficient numerical method for the distributed order time-fractional diffusion equation with error analysis and stability. Mathematics and Computers in Simulation 214, pages 315-333.
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Jiashu Lu, Qingyu Zhang, Lijing Zhao & Yufeng Nie. (2023) An Efficient Jacobi Spectral Collocation Method with Nonlocal Quadrature Rules for Multi-Dimensional Volume-Constrained Nonlocal Models. International Journal of Computational Methods 20:05.
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Zhiwei Yang & Hong Wang. (2023) A distributed‐order fractional diffusion equation with a singular density function: Analysis and approximation. Mathematical Methods in the Applied Sciences 46:8, pages 9819-9833.
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Xuan Zhao, Xiaoli Li & Ziyan Li. (2022) Fast and efficient finite difference method for the distributed-order diffusion equation based on the staggered grids. Applied Numerical Mathematics 174, pages 34-45.
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S. Hadi Seyedi & Mohsen Zayernouri. (2022) A data-driven dynamic nonlocal subgrid-scale model for turbulent flows. Physics of Fluids 34:3.
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Nischay Rai & Sabyasachi Mondal. (2021) Spectral methods to solve nonlinear problems: A review. Partial Differential Equations in Applied Mathematics 4, pages 100043.
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Farhad Fakhar-Izadi. (2020) Fully Petrov–Galerkin spectral method for the distributed-order time-fractional fourth-order partial differential equation. Engineering with Computers 37:4, pages 2707-2716.
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Jianfei Huang, Jingna Zhang, Sadia Arshad & Yifa Tang. (2021) A superlinear convergence scheme for the multi‐term and distribution‐order fractional wave equation with initial singularity. Numerical Methods for Partial Differential Equations 37:4, pages 2833-2848.
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Quan H. Do, Hoa T.B. Ngo & Mohsen Razzaghi. (2021) A generalized fractional-order Chebyshev wavelet method for two-dimensional distributed-order fractional differential equations. Communications in Nonlinear Science and Numerical Simulation 95, pages 105597.
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Nasrin Moshtaghi & Abbas Saadatmandi. (2021) Polynomial–Sinc collocation method combined with the Legendre–Gauss quadrature rule for numerical solution of distributed order fractional differential equations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 115:2.
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Mehdi Samiee, Ehsan Kharazmi, Mark M. Meerschaert & Mohsen Zayernouri. (2020) A Unified Petrov–Galerkin Spectral Method and Fast Solver for Distributed-Order Partial Differential Equations. Communications on Applied Mathematics and Computation 3:1, pages 61-90.
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Boonrod Yuttanan, Mohsen Razzaghi & Thieu N. Vo. (2021) A numerical method based on fractional-order generalized Taylor wavelets for solving distributed-order fractional partial differential equations. Applied Numerical Mathematics 160, pages 349-367.
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Wei Ding, Sansit Patnaik, Sai Sidhardh & Fabio Semperlotti. (2021) Applications of Distributed-Order Fractional Operators: A Review. Entropy 23:1, pages 110.
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Afshin Babaei, Seddigheh Banihashemi & Carlo Cattani. (2020) An efficient numerical approach to solve a class of variable‐order fractional integro‐partial differential equations. Numerical Methods for Partial Differential Equations 37:1, pages 674-689.
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Yashveer Kumar, Somveer Singh, Nikhil Srivastava, Aman Singh & Vineet Kumar Singh. (2020) Wavelet approximation scheme for distributed order fractional differential equations. Computers & Mathematics with Applications 80:8, pages 1985-2017.
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Yongtao Zhou, Jorge L. Suzuki, Chengjian Zhang & Mohsen Zayernouri. (2020) Implicit-explicit time integration of nonlinear fractional differential equations. Applied Numerical Mathematics 156, pages 555-583.
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Mahmoud A. Zaky & J. Tenreiro Machado. (2020) Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations. Computers & Mathematics with Applications 79:2, pages 476-488.
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Marzieh Pourbabaee & Abbas Saadatmandi. (2019) A novel Legendre operational matrix for distributed order fractional differential equations. Applied Mathematics and Computation 361, pages 215-231.
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Mahmoud A. Zaky. (2019) Recovery of high order accuracy in Jacobi spectral collocation methods for fractional terminal value problems with non-smooth solutions. Journal of Computational and Applied Mathematics 357, pages 103-122.
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Xiangcheng Zheng, Huan Liu, Hong Wang & Hongfei Fu. (2019) An Efficient Finite Volume Method for Nonlinear Distributed-Order Space-Fractional Diffusion Equations in Three Space Dimensions. Journal of Scientific Computing 80:3, pages 1395-1418.
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Ehsan Kharazmi & Mohsen Zayernouri. (2019) Fractional Sensitivity Equation Method: Application to Fractional Model Construction. Journal of Scientific Computing 80:1, pages 110-140.
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Mehdi Samiee, Mohsen Zayernouri & Mark M. Meerschaert. (2019) A unified spectral method for FPDEs with two-sided derivatives; Part II: Stability, and error analysis. Journal of Computational Physics 385, pages 244-261.
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