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Variable-order fractional differential operators in anomalous diffusion modeling

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Cited by:

  1. Chauhan, Archana & Gautam, G.R. & Chauhan, S.P.S. & Dwivedi, Arpit, 2023. "A validation on concept of formula for variable order integral and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
  2. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
  3. Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
  4. Hamid, M. & Usman, M. & Haq, R.U. & Wang, W., 2020. "A Chelyshkov polynomial based algorithm to analyze the transport dynamics and anomalous diffusion in fractional model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
  5. Souad Bensid Ahmed & Adel Ouannas & Mohammed Al Horani & Giuseppe Grassi, 2022. "The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
  6. Jahanshahi, Hadi & Sajjadi, Samaneh Sadat & Bekiros, Stelios & Aly, Ayman A., 2021. "On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
  7. Wei, Leilei & Li, Wenbo, 2021. "Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo–Fabrizio fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 280-290.
  8. Zahra, Waheed K. & Abdel-Aty, Mahmoud & Abidou, Diaa, 2020. "A fractional model for estimating the hole geometry in the laser drilling process of thin metal sheets," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
  9. Zhang, Yong & Sun, HongGuang & Stowell, Harold H. & Zayernouri, Mohsen & Hansen, Samantha E., 2017. "A review of applications of fractional calculus in Earth system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 29-46.
  10. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
  11. Qu, Hai-Dong & Liu, Xuan & Lu, Xin & ur Rahman, Mati & She, Zi-Hang, 2022. "Neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
  12. Yin, Deshun & Wang, Yixin & Li, Yanqing & Cheng, Chen, 2013. "Variable-order fractional mean square displacement function with evolution of diffusibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4571-4575.
  13. Ruilian Du & Zongqi Liang, 2017. "Two New Approximations for Variable-Order Fractional Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-10, July.
  14. Yang, Zhiwei & Zheng, Xiangcheng & Zhang, Zhongqiang & Wang, Hong, 2021. "Strong convergence of a Euler-Maruyama scheme to a variable-order fractional stochastic differential equation driven by a multiplicative white noise," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
  15. Liu, Lu & Xue, Dingyu & Zhang, Shuo, 2019. "Closed-loop time response analysis of irrational fractional-order systems with numerical Laplace transform technique," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 133-152.
  16. Meng, Ruifan & Yin, Deshun & Yang, Haixia & Xiang, Guangjian, 2020. "Parameter study of variable order fractional model for the strain hardening behavior of glassy polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
  17. Hasib Khan & Jehad Alzabut & Haseena Gulzar & Osman Tunç & Sandra Pinelas, 2023. "On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
  18. Heydari, M.H. & Avazzadeh, Z. & Mahmoudi, M.R., 2019. "Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 105-124.
  19. Zhang, Jiali & Fang, Zhi-Wei & Sun, Hai-Wei, 2022. "Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions," Applied Mathematics and Computation, Elsevier, vol. 430(C).
  20. Eftekhari, Tahereh & Rashidinia, Jalil, 2022. "A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 429(C).
  21. Pu, Zhe & Ran, Maohua & Luo, Hong, 2021. "Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 110-133.
  22. Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Viet-Thanh Pham, 2020. "On the Stability of Linear Incommensurate Fractional-Order Difference Systems," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
  23. Al-Mdallal, Qasem M. & Abu Omer, Ahmed S., 2018. "Fractional-order Legendre-collocation method for solving fractional initial value problems," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 74-84.
  24. Mian Bahadur Zada & Muhammad Sarwar & Thabet Abdeljawad & Aiman Mukheimer, 2021. "Coupled Fixed Point Results in Banach Spaces with Applications," Mathematics, MDPI, vol. 9(18), pages 1-12, September.
  25. Straka, Peter, 2018. "Variable order fractional Fokker–Planck equations derived from Continuous Time Random Walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 451-463.
  26. Guo, Gang & Li, Kun & Wang, Yuhui, 2015. "Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 193-201.
  27. Atangana, Abdon & Shafiq, Anum, 2019. "Differential and integral operators with constant fractional order and variable fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 226-243.
  28. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
  29. Li, Qiaoping & Liu, Sanyang & Chen, Yonggang, 2018. "Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 521-535.
  30. Mohammed K. A. Kaabar & Ahmed Refice & Mohammed Said Souid & Francisco Martínez & Sina Etemad & Zailan Siri & Shahram Rezapour, 2021. "Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
  31. Chang, Ailian & Sun, HongGuang & Zheng, Chunmiao & Lu, Bingqing & Lu, Chengpeng & Ma, Rui & Zhang, Yong, 2018. "A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 356-369.
  32. Hayman Thabet & Subhash Kendre & Dimplekumar Chalishajar, 2017. "New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-15, September.
  33. Hossein Fazli & HongGuang Sun & Juan J. Nieto, 2020. "Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
  34. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
  35. Li, Zheng & Wang, Hong & Xiao, Rui & Yang, Su, 2017. "A variable-order fractional differential equation model of shape memory polymers," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 473-485.
  36. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
  37. Heydari, Mohammad Hossein & Avazzadeh, Zakieh & Haromi, Malih Farzi, 2019. "A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 215-228.
  38. Tabatabaei, S. Sepehr & Talebi, H.A. & Tavakoli, M., 2017. "A novel adaptive order/parameter identification method for variable order systems application in viscoelastic soft tissue modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 447-455.
  39. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
  40. Heydari, Mohammad Hossein & Avazzadeh, Zakieh, 2018. "Legendre wavelets optimization method for variable-order fractional Poisson equation," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 180-190.
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