The lack of a general nonlinear space-time fractional
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The lack of a general nonlinear space-time fractional formulation of the Fokker-Planck equation. The need for exact analytical solutions for such a model.
Evidence profile
Sourced from the stated research gap of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 3 representative gaps
- Comparative semi-analytical solutions of Caputo time-fractional Fokker–Planck equations via Laplace transform–based decomposition and iterative methods (2026) · DOAJ (DOAJ: Directory of Open Access Journals) · doi
There is a need for efficient and accurate methods for solving time-fractional Fokker-Planck equations. The existing methods have limitations, such as requiring linearization, discretization, or perturbation.
generalstated research gapKeywords: there need efficient accurate methods solving time-fractional fokker-planck - On solutions of space-time fractional nonlinear Fokker–Planck equation. II (2026) · Fractional Calculus and Applied Analysis · doi
The lack of a general nonlinear space-time fractional formulation of the Fokker-Planck equation. The need for exact analytical solutions for such a model.
generalstated research gapevidence 5/5Keywords: lack general nonlinear space-time fractional formulation fokker-planck equation - Stochastic numerical approximation for nonlinear Fokker-Planck equations with singular kernels (2026) · Stochastic Partial Differential Equations Analysis and Computations · doi
The convergence of numerical schemes for nonlinear Fokker-Planck equations with singular kernels is not well understood. Existing results do not apply to singular kernels.
generalstated research gapevidence 3/5Keywords: convergence numerical schemes nonlinear fokker-planck equations singular kernels
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