Most cited papers in Fractional Differential Equations Solutions
What are the most cited papers in Fractional Differential Equations Solutions?
The most cited paper in Fractional Differential Equations Solutions is "The random walk's guide to anomalous diffusion: a fractional dynamics approach" (Ralf Metzler, J. Klafter, 2000), with 9,129 citations. Next come "Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon" (5,387) and "User’s guide to viscosity solutions of second order partial differential equations" (5,020).
Showing 50 of 100 papers. Every paper with more than 810 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | The random walk's guide to anomalous diffusion: a fractional dynamics approach Ralf Metzler, J. Klafter · Physics Reports | Dec 2000 | 9,129 |
| 2 | Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon Thomas A. Witten, Leonard M. Sander · Physical Review Letters | 9 Nov 1981 | 5,387 |
| 3 | User’s guide to viscosity solutions of second order partial differential equations Michael G. Crandall, Hitoshi Ishii, Pierre-Louis Lions · Bulletin of the American Mathematical Society | 1992 | 5,020 |
| 4 | Dual variational methods in critical point theory and applications Antonio Ambrosetti, Paul H. Rabinowitz · Journal of Functional Analysis | Dec 1973 | 4,419 |
| 5 | On certain integrals of Lipschitz-Hankel type involving products of bessel functions G. Eason, Ben Noble, Ian Naismith Sneddon · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences | 19 Apr 1955 | 4,401 |
| 6 | Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications Jean‐Philippe Bouchaud, Antoine Georges · Physics Reports | Nov 1990 | 4,213 |
| 7 | New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model Atangana Abdon, Dumitru Bǎleanu · DOAJ (DOAJ: Directory of Open Access Journals) | 2016 | 3,956 |
| 8 | Mean shift, mode seeking, and clustering Yizong Cheng · IEEE Transactions on Pattern Analysis and Machine Intelligence | 1995 | 3,912 |
| 9 | A new definition of fractional derivative Roshdi Rashid Khalil, Mohammed Al Horani, A. Yousef et al. · Journal of Computational and Applied Mathematics | 16 Jan 2014 | 3,504 |
| 10 | Homotopy perturbation technique Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering | Aug 1999 | 3,485 |
| 11 | Analysis of Fractional Differential Equations Kai Diethelm, Neville J. Ford · Journal of Mathematical Analysis and Applications | 2002 | 3,200 |
| 12 | Meshless methods: An overview and recent developments Ted Belytschko, Y. Krongauz, D. Organ et al. · Computer Methods in Applied Mechanics and Engineering | Dec 1996 | 3,147 |
| 13 | Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers Igor Podlubný · IEEE Transactions on Automatic Control | 1999 | 3,112 |
| 14 | Beyond Perturbation: Introduction to the Homotopy Analysis Method Shijun Liao,, S. A. Sherif · Applied Mechanics Reviews | Sep 2004 | 2,705 |
| 15 | Variational iteration method – a kind of non-linear analytical technique: some examples Ji‐Huan He · International Journal of Non-Linear Mechanics | Jul 1999 | 2,553 |
| 16 | The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics Ralf Metzler, J. Klafter · Journal of Physics A Mathematical and General | 21 Jul 2004 | 2,390 |
| 17 | An Extension Problem Related to the Fractional Laplacian Luis Caffarelli, Luis Silvestre · Communications in Partial Differential Equations | 8 Aug 2007 | 2,342 |
| 18 | SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS Ji‐Huan He · International Journal of Modern Physics B | 19 Apr 2006 | 2,215 |
| 19 | The topological theory of defects in ordered media N. David Mermin · Reviews of Modern Physics | Jul 1979 | 2,213 |
| 20 | On conformable fractional calculus Thabet Abdeljawad · Journal of Computational and Applied Mathematics | 29 Oct 2014 | 2,054 |
| 21 | Extended tanh-function method and its applications to nonlinear equations Engui Fan · Physics Letters A | Dec 2000 | 2,024 |
| 22 | Fractional Calculus in Bioengineering Bruce J. West · Journal of Statistical Physics | 12 Feb 2007 | 1,999 |
| 23 | Exp-function method for nonlinear wave equations Ji‐Huan He, Xuhong Wu · Chaos Solitons & Fractals | 3 May 2006 | 1,981 |
| 24 | A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity Ronald L. Bagley, Peter J. Torvik · Journal of Rheology | Jun 1983 | 1,961 |
| 25 | The ()-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics Mingliang Wang, Xiangzheng Li, Jinliang Zhang · Physics Letters A | 2 Aug 2007 | 1,948 |
| 26 | Multidimensional nonlinear diffusion arising in population genetics D. G. Aronson, Hans F. Weinberger · Advances in Mathematics | Oct 1978 | 1,939 |
| 27 | Finite difference/spectral approximations for the time-fractional diffusion equation Yumin Lin, Chuanju Xu · Journal of Computational Physics | 15 Feb 2007 | 1,843 |
| 28 | Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking Ralf Metzler, Jae‐Hyung Jeon, Andrey G. Cherstvy et al. · Physical Chemistry Chemical Physics | 2014 | 1,842 |
| 29 | A coupling method of a homotopy technique and a perturbation technique for non-linear problems Ji‐Huan He · International Journal of Non-Linear Mechanics | 2000 | 1,811 |
| 30 | On the homotopy analysis method for nonlinear problems Shijun Liao · Applied Mathematics and Computation | 11 Oct 2003 | 1,787 |
| 31 | A new collection of real world applications of fractional calculus in science and engineering HongGuang Sun, Yong Zhang, Dumitru Bǎleanu et al. · Communications in Nonlinear Science and Numerical Simulation | 24 Apr 2018 | 1,786 |
| 32 | The Fractional Order Fourier Transform and its Application to Quantum Mechanics Victor Namias · IMA Journal of Applied Mathematics | 1980 | 1,722 |
| 33 | Chaos, fractional kinetics, and anomalous transport G. M. Zaslavsky · Physics Reports | Dec 2002 | 1,640 |
| 34 | Recent history of fractional calculus J. A. Tenreiro Machado, Virginia S. Kiryakova, Francesco Mainardi · Communications in Nonlinear Science and Numerical Simulation | Jun 2010 | 1,638 |
| 35 | Mittag–Leffler stability of fractional order nonlinear dynamic systems Yan Li, YangQuan Chen, Igor Podlubný · Automatica | 14 May 2009 | 1,634 |
| 36 | Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability Yan Li, YangQuan Chen, Igor Podlubný · Computers & Mathematics with Applications | 29 Aug 2009 | 1,620 |
| 37 | Homotopy perturbation method: a new nonlinear analytical technique Ji‐Huan He · Applied Mathematics and Computation | 7 Oct 2002 | 1,616 |
| 38 | Fractional quantum mechanics and Lévy path integrals Nikolai Laskin · Physics Letters A | Apr 2000 | 1,604 |
| 39 | Fractional Schrödinger equation Nick Laskin · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics | 18 Nov 2002 | 1,588 |
| 40 | Finite difference approximations for fractional advection–dispersion flow equations Mark M. Meerschaert, Charles Tadjeran · Journal of Computational and Applied Mathematics | 17 Mar 2004 | 1,509 |
| 41 | Accurate solution of the Orr–Sommerfeld stability equation Steven A. Orszag · Journal of Fluid Mechanics | 29 Dec 1971 | 1,483 |
| 42 | Lyapunov functions for fractional order systems Norelys Aguila‐Camacho, Manuel A. Duarte‐Mermoud, Javier A. Gallegos · Communications in Nonlinear Science and Numerical Simulation | 3 Feb 2014 | 1,472 |
| 43 | Applications of Fractional Calculus to the Theory of Viscoelasticity R. C. Koeller · Journal of Applied Mechanics | Jun 1984 | 1,448 |
| 44 | The role of constraints within generalized nonextensive statistics Constantino Tsallis, RenioS. Mendes, Angel R. Plastino · Physica A Statistical Mechanics and its Applications | Dec 1998 | 1,444 |
| 45 | Stability results for fractional differential equations with applications to control processing Denis Matignon | 1996 | 1,442 |
| 46 | A generalization of the Kermack-McKendrick deterministic epidemic model Vincenzo Capasso, Gabriella Serio · Mathematical Biosciences | Nov 1978 | 1,316 |
| 47 | Approximate analytical solution for seepage flow with fractional derivatives in porous media Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering | Dec 1998 | 1,298 |
| 48 | A Caputo fractional derivative of a function with respect to another function Ricardo Almeida · Communications in Nonlinear Science and Numerical Simulation | 12 Sep 2016 | 1,283 |
| 49 | A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations Kai Diethelm, Neville J. Ford, Alan D. Freed · Nonlinear Dynamics | Jul 2002 | 1,275 |
| 50 | Anomalous transport in the crowded world of biological cells Felix Höfling, Thomas Franosch · Reports on Progress in Physics | 12 Mar 2013 | 1,273 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.