A review of applications of fractional calculus in Earth system dynamics
Author
Abstract
Suggested Citation
DOI: 10.1016/j.chaos.2017.03.051
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- C. Beaumont & R. A. Jamieson & M. H. Nguyen & B. Lee, 2001. "Himalayan tectonics explained by extrusion of a low-viscosity crustal channel coupled to focused surface denudation," Nature, Nature, vol. 414(6865), pages 738-742, December.
- John E. Vidale & Doug A. Dodge & Paul S. Earle, 2000. "Slow differential rotation of the Earth's inner core indicated by temporal changes in scattering," Nature, Nature, vol. 405(6785), pages 445-448, May.
- P. Hersen, 2004. "On the crescentic shape of barchan dunes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 37(4), pages 507-514, February.
- Bolster, Diogo & Benson, David A. & Meerschaert, Mark M. & Baeumer, Boris, 2013. "Mixing-driven equilibrium reactions in multidimensional fractional advection–dispersion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2513-2525.
- Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
- David Bercovici & Shun-ichiro Karato, 2003. "Whole-mantle convection and the transition-zone water filter," Nature, Nature, vol. 425(6953), pages 39-44, September.
- Veit Schwämmle & Hans J. Herrmann, 2003. "Solitary wave behaviour of sand dunes," Nature, Nature, vol. 426(6967), pages 619-620, December.
- Pei-Ying Patty Lin & James B. Gaherty & Ge Jin & John A. Collins & Daniel Lizarralde & Rob. L. Evans & Greg Hirth, 2016. "High-resolution seismic constraints on flow dynamics in the oceanic asthenosphere," Nature, Nature, vol. 535(7613), pages 538-541, July.
- Tarasov, Vasily E., 2014. "Flow of fractal fluid in pipes: Non-integer dimensional space approach," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 26-37.
- Lima, A.R & Sauermann, G & Herrmann, H.J & Kroy, K, 2002. "Modelling a dune field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 487-500.
- Weijia Kuang & Jeremy Bloxham, 1997. "An Earth-like numerical dynamo model," Nature, Nature, vol. 389(6649), pages 371-374, September.
- Lim, C.Y. & Meerschaert, M.M. & Scheffler, H.-P., 2014. "Parameter estimation for operator scaling random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 172-183.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
- Yong Zhang & Dongbao Zhou & Wei Wei & Jonathan M. Frame & Hongguang Sun & Alexander Y. Sun & Xingyuan Chen, 2021. "Hierarchical Fractional Advection-Dispersion Equation (FADE) to Quantify Anomalous Transport in River Corridor over a Broad Spectrum of Scales: Theory and Applications," Mathematics, MDPI, vol. 9(7), pages 1-15, April.
- Huang, Chi-Hsiang & Tsai, Christina W. & Wu, Kuan-Ting, 2020. "Estimation of near-bed sediment concentrations in turbulent flow beyond normality," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
- Adán J. Serna-Reyes & Jorge E. Macías-Díaz & Nuria Reguera, 2021. "A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
- Shen, Stanley W. & Tsai, Christina W., 2024. "Incorporating memory effect into a fractional stochastic diffusion particle tracking model for suspended sediment using Malliavin-Calculus-based fractional Brownian Motion," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
- Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2022. "An efficient numerical scheme for fractional characterization of MHD fluid model," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
- Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
- Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2023. "A computational numerical algorithm for thermal characterization of fractional unsteady free convection flow in an open cavity," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
- Bingqing Lu & Yong Zhang & Donald M. Reeves & HongGuang Sun & Chunmiao Zheng, 2018. "Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks," Mathematics, MDPI, vol. 6(1), pages 1-16, January.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Robson, Dominic T. & Annibale, Alessia & Baas, Andreas C.W., 2022. "Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
- 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.
- 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).
- 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).
- 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.
- 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).
- 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).
- 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).
- 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.
- 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).
- 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).
- Shi, Feng & Huang, Ning, 2012. "Measurement and simulation of sand saltation movement under fluctuating wind in a natural field environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 474-484.
- 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).
- Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
- Zhipeng Zhou & Hans Thybo & Irina M. Artemieva & Timothy Kusky & Chi-Chia Tang, 2024. "Crustal melting and continent uplift by mafic underplating at convergent boundaries," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
- 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.
- 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.
- HASSANE GANDA Rabi & HAMIDOU Haoua & SALEY Bisso, 2017. "Modeling and Numerical Simulation of Sand Dunes Formation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 78-86, August.
- 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).
- Xiaoping Yuan & Yuqiang Li & Sascha Brune & Kai Li & Michaël Pons & Sebastian G. Wolf, 2024. "Coordination between deformation, precipitation, and erosion during orogenic growth," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
More about this item
Keywords
Fractional calculus; Fractional derivative models; Hydrologic processes; Solid Earth;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:29-46. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.