Original Research Open access Published: 29 Jul 2026

An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics

Masood Rauf khan

National Research Council Institute for SuPerconductors, INnovative Materials, and Devices, CNR-SPIN, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy.

Journal of Computational Mathematics and Physics volume 1 pages 28-42 (2026)

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Received 12 Apr 2026 Revised 12 Jul 2026 Accepted 19 Jul 2026 Published 29 Jul 2026 License CC BY 4.0

Keywords: Fractional partial differential equations; Physics-informed neural networks; Caputo derivative; Inverse problems; error analysis; anomalous diffusion; scientific machine learning.

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khan, M. R. An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics. J. Comp. Math. Phy. 1, 28–42 (2026). http://jcmp.org/articles/2026-1-1-003

khan, M. R. (2026). An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics. Journal of Computational Mathematics and Physics, 1(1), 28–42. http://jcmp.org/articles/2026-1-1-003

Masood Rauf khan. "An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics." Journal of Computational Mathematics and Physics, vol. 1, no. 1, 2026, pp. 28–42, http://jcmp.org/articles/2026-1-1-003.

Masood Rauf khan. "An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics." Journal of Computational Mathematics and Physics 1, no. 1 (2026): 28–42. http://jcmp.org/articles/2026-1-1-003.

khan MR. An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics. J. Comp. Math. Phy.. 2026;1(1):28-42. Available from: http://jcmp.org/articles/2026-1-1-003

@article{khan2026anuncertaintyaware,
  title = {An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics},
  author = {khan, Masood Rauf},
  journal = {Journal of Computational Mathematics and Physics},
  year = {2026},
  volume = {1},
  number = {1},
  pages = {28--42},
  url = {http://jcmp.org/articles/2026-1-1-003},
}