Evidence map›Paper›PMID 41936611›Full record

ArticleScientific reports2026

Fuzzy fractional modeling and analysis of stochastic Fokker Planck equations under uncertainty and memory effects.

Mubashir Qayyum, Warda Rashid, Faisal Z Duraihem, Efaza Ahmad, Omar Khan, Syed Tauseef Saeed, Feyisa Edosa Merga

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Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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1 · What the graph read from it

What it found

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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

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3 · Its place in the literature

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4 · The record

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5 · Who and what money

Authors and funding

7 authors.

Mubashir QayyumDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences Lahore Campus, Lahore, Pakistan.
Warda RashidDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences Lahore Campus, Lahore, Pakistan.
Faisal Z DuraihemDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia.
Efaza AhmadDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences Lahore Campus, Lahore, Pakistan.
Omar KhanDepartment of Computer Science, National University of Computer and Emerging Sciences Peshawar Campus, Peshawar, Pakistan.
Syed Tauseef SaeedDepartment of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan. tauseef.saeed@math.uol.edu.pk.
Feyisa Edosa MergaDepartment of Mathematics, Jimma University, Jimma, Ethiopia. edosa.feyisa@ju.edu.et.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

In this study, the Fokker-Planck model, which describes the time-evolution of probability density functions, is reformulated within a fuzzy-fractional structure to incorporate uncertainties. Triangular fuzzy numbers are employed to represent uncertainty by incorporating fuzzy parameter in the initial conditions. After fuzzification, He-Laplace framework is applied to derive approximate analytical solutions. To evaluate the efficiency and reliability of the proposed methodology, residual errors are computed for both upper and lower bound solutions. The numerical results are further analyzed numerically through comparative tables, and visually as 2D, 3D and contour plots. The results demonstrate that the observed errors remain negligible, supporting the efficacy of proposed methodology and validity of obtained solutions. The proposed framework provides an efficient tool for analyzing fuzzy–fractional Fokker–Planck models and can be extended to other nonlinear fuzzy fractional systems.

Indexed as

Caputo derivativeFokker–Planck equationsFuzzy-fractional modelingHe-Laplace algorithmTriangular fuzzy number

Identifiers

PMID41936611
PMCPMC13212668

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