Leaderboards/Differential Equations and Numerical Methods

Differential Equations and Numerical Methods

Last updated July 7, 2026

Rising Stars

New and hot

Rising Stars Researchers

1
Sudarshan Santra
Indian Institute of Science Bangalore
2
Xiao-Tian Gao
Beijing University of Posts and Telecommunications
3
Dianming Hou
Jiangsu Normal University
4
Haneen Badawi
Palestine Technical University - Kadoorie
5
Hind Sweis
University of Jordan
6
Sumit Saini
Central University of Haryana
7
Fukeng Huang
Bridge University
8
Qing Cheng
Tongji University
9
Naol Tufa Negero
Wollega University
10
Marimuthu Mohan Raja
Kyungpook National University

Rising Stars Papers

1
N-soliton, Hth-order breather, hybrid and multi-pole solutions for a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid
Nonlinear Dynamics|2024
154 cit.
2
Bilinear Bäcklund Transformations, as well as N-Soliton, Breather, Fission/Fusion and Hybrid Solutions for a (3+1)-Dimensional Integrable Wave Equation in a Fluid
Qualitative Theory of Dynamical Systems|2025
124 cit.
3
Similarity Reductions on a (2$$+$$1)-Dimensional Variable-Coefficient Modified Kadomtsev-Petviashvili System Describing Certain Electromagnetic Waves in a Thin Film
International Journal of Theoretical Physics|2024
96 cit.
4
Bilinear Form, N Solitons, Breathers and Periodic Waves for a (3+1)-Dimensional Korteweg-de Vries Equation with the Time-Dependent Coefficients in a Fluid
Qualitative Theory of Dynamical Systems|2024
38 cit.
5
Existence, uniqueness, and galerkin shifted Legendre's approximation of time delays integrodifferential models by adapting the Hilfer fractional attitude
Heliyon|2024
31 cit.
6
Existence, uniqueness, and collocation solutions using the shifted Legendre spectral method for the Hilfer fractional stochastic integro-differential equations regarding stochastic Brownian motion
Results in Applied Mathematics|2024
29 cit.
7
Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set
PLoS ONE|2024
22 cit.
8
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels
Numerical Algorithms|2024
19 cit.
9
Painlevé Analysis, Bilinear Forms, Bäcklund Transformations and Solitons for a Variable-Coefficient Extended Korteweg-de Vries Equation with an External-Force Term in Fluid Mechanics and Plasma Dynamics
Qualitative Theory of Dynamical Systems|2024
15 cit.
10
A Linear Doubly Stabilized Crank-Nicolson Scheme for the Allen–Cahn Equation with a General Mobility
Advances in Applied Mathematics and Mechanics|2024
14 cit.

Emerging Leaders

Gaining momentum

Emerging Leaders Researchers

1
Omar Bazighifan
University of Aden
2
Nasrin Samadyar
Kermanshah University of Technology
3
Wenlin Qiu
Hunan Normal University
4
Hijaz Ahmad
Korea University
5
Xiangcheng Zheng
Shandong University
6
Ali Muhib
Jadara University
7
Juan Pablo Borthagaray
Universidad de la República de Uruguay
8
Ranbir Kumar
Birla Institute of Technology, Mesra
9
Babak Shiri
University of Tabriz
10
Banan Maayah
University of Jordan

Emerging Leaders Papers

1
Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme
Chinese Journal of Physics|2022
143 cit.
2
The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach
Demonstratio Mathematica|2022
143 cit.
3
Enhancing catalytic activity of gold nanoparticles in a standard redox reaction by investigating the impact of AuNPs size, temperature and reductant concentrations
Scientific Reports|2023
101 cit.
4
Adaptive the Dirichlet model of mobile/immobile advection/dispersion in a time-fractional sense with the reproducing kernel computational approach: Formulations and approximations
International Journal of Modern Physics B|2022
82 cit.
5
MHD nanofluid flow and heat transfer caused by a stretching sheet that is heated convectively: An approximate solution using ADM
Case Studies in Thermal Engineering|2024
67 cit.
6
Fuzzy M-fractional integrodifferential models: theoretical existence and uniqueness results, and approximate solutions utilizing the Hilbert reproducing kernel algorithm
Frontiers in Physics|2023
62 cit.
7
A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
AIMS Mathematics|2023
59 cit.
8
Generalized fractional differential equations for past dynamic
AIMS Mathematics|2022
49 cit.
9
New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena
Results in Physics|2022
47 cit.
10
Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems
Computational and Applied Mathematics|2022
45 cit.

Current Senior Leaders

Established & currently active

Current Senior Leaders Researchers

1
Dumitru Bǎleanu
Lebanese American University
2
Mehdi Dehghan
Amirkabir University of Technology
3
Neville J. Ford
University of Chester
4
Zhi‐zhong Sun
Southeast University
5
Donal O’Regan
National University of Ireland
6
Darryl D. Holm
Imperial College London
7
Fawang Liu
Queensland University of Technology
8
Juan J. Nieto
Universidade de Santiago de Compostela
9
Chuanju Xu
Jingdezhen University
10
Ian Turner
Queensland University of Technology

Current Senior Leaders Papers

1
New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model
DOAJ (DOAJ: Directory of Open Access Journals)|2016
3.9k cit.
2
An integrable shallow water equation with peaked solitons
Physical Review Letters|1993
3.7k cit.
3
Analysis of Fractional Differential Equations
Journal of Mathematical Analysis and Applications|2002
3.2k cit.
4
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics|2007
1.8k cit.
5
Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations
Order|2005
1.3k cit.
6
A fully discrete difference scheme for a diffusion-wave system
Applied Numerical Mathematics|2005
1.2k cit.
7
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories
Advances in Mathematics|1998
998 cit.
8
Nonlinear stability of fluid and plasma equilibria
Physics Reports|1985
893 cit.
9
A new operational matrix for solving fractional-order differential equations
Computers & Mathematics with Applications|2009
793 cit.
10
A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative
Chaos Solitons & Fractals|2020
764 cit.

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