Fractional Differential Equations Solutions
Fractional Differential Equations Solutions is a research topic within Modeling and Simulation. Science Explorer counts 37k research works in it since 1951. 20.1% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on the modeling, analysis, and applications of anomalous diffusion using fractional calculus, nonlinear equations, and the homotopy analysis method. It explores phenomena such as random walk, fractional derivatives, time-fractional diffusion equations, single particle tracking in biological cells, and diffusion in crowded environments.
- Anomalous Diffusion
- Fractional Calculus
- Nonlinear Equations
- Homotopy Analysis Method
- Random Walk
- Fractional Derivatives
- Time-Fractional Diffusion Equation
- Single Particle Tracking
- Biological Cells
- Crowded Environments
- Research works
- 37k fractional, since 1951
- In the world top 10%
- 7.4k per year above
- Top-10% rate
- 20.1% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +63% the tick is no change
Which countries lead Fractional Differential Equations Solutions research?
By volume, China and India publish the most (2k and 1.2k works in 2022–2025).
By volume, 2022–2025
- 1 China 2k works
- 2 India 1.2k works
- 3 Saudi Arabia 792 works
- 4 Türkiye 500 works
- 5 Pakistan 488 works
- 6 Iran 404 works
- 7 Egypt 331 works
- 8 United States 322 works
- 9 Iraq 257 works
- 10 Algeria 209 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Fractional Differential Equations Solutions research?
By volume in 2022–2025, Vellore Institute of Technology University publishes the most Fractional Differential Equations Solutions research, followed by King Saud University and King Abdulaziz University.
By volume, 2022–2025
- 1 Vellore Institute of Technology UniversityIndia 76 works
- 2 King Saud UniversitySaudi Arabia 65 works
- 3 King Abdulaziz UniversitySaudi Arabia 63 works
- 4 Université Sultan Moulay SlimaneMorocco 58 works
- 5 Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 58 works
- 6 China Medical UniversityTaiwan 50 works
- 7 Qassim UniversitySaudi Arabia 49 works
- 8 Henan Polytechnic UniversityChina 48 works
- 9 Imam Mohammad ibn Saud Islamic UniversitySaudi Arabia 45 works
- 10 Prince Sultan UniversitySaudi Arabia 44 works
Who are the leading researchers in Fractional Differential Equations Solutions?
The most-cited researchers publishing on Fractional Differential Equations Solutions include George Em Karniadakis, Guanrong Chen and Tasawar Hayat.
- 1 George Em Karniadakis United States 6.3k citations
- 2 Guanrong Chen Hong Kong 5.4k citations
- 3 Tasawar Hayat Pakistan 4.6k citations
- 4 Jinde Cao China 4.2k citations
- 5 Timon Rabczuk Germany 2.7k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Fractional Differential Equations Solutions research done?
The largest centres of Fractional Differential Equations Solutions research in 2022–2025 are Riyadh (Saudi Arabia), Beijing (China), Cairo (Egypt) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Malakand and Beni Mellal.
Largest cities, 2022–2025
Where it is the local speciality
- MalakandPK · 34.6 works76×
- Beni MellalMA · 58.2 works45×
Location quotient: how much more of its research is in Fractional Differential Equations Solutions than the world average.
Where is the best place to study Fractional Differential Equations Solutions?
Among universities, judged by research, Prince Sattam Bin Abdulaziz University, Prince Sultan University and Henan Polytechnic University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Prince Sattam Bin Abdulaziz UniversitySaudi Arabia | 82.1 | 38.8% | 23.7× | 58 | +653.2% |
| 2 | Prince Sultan UniversitySaudi Arabia | 80.5 | 39.8% | 42.5× | 44 | +954.7% |
| 3 | Henan Polytechnic UniversityChina | 80.1 | 57.1% | 17.6× | 48 | +804.8% |
| 4 | University of MalakandPakistan | 75.3 | 37.4% | 75.7× | 35 | +299.8% |
| 5 | Taibah UniversitySaudi Arabia | 73.9 | 41.0% | 17.1× | 25 | +291.3% |
| 6 | Lebanese American UniversityLebanon | 73.6 | 42.8% | 41.9× | 44 | — |
| 7 | King Khalid UniversitySaudi Arabia | 73.5 | 32.2% | 11.9× | 41 | +137.3% |
| 8 | Imam Mohammad ibn Saud Islamic UniversitySaudi Arabia | 71.1 | 24.4% | 25.4× | 45 | +167.0% |
| 9 | Al-Balqa Applied UniversityJordan | 70.7 | 42.3% | 26.5× | 27 | +176.2% |
| 10 | University of the PunjabPakistan | 70.1 | 42.9% | 9.3× | 26 | +199.3% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Fractional Differential Equations Solutions research growing?
Output in 2018–2022 was 63% higher than in 2013–2017, peaking in 2022. The fastest-growing topics are Fractional Differential Equations Solutions.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.