Original Research Open access Published: 9 Jul 2026

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

Muhammad Umar

Center for Applied Mathematics and Bioinformatics, Department of Mathematics and Natural Sciences, Gulf University for Science and Technology Mubarak Al-Abdullah Area/West Mishref, Kuwait.
The CA-AD Group, Heidelberg University, Germany .

Journal of Computational Mathematics and Physics volume 1 pages 11-27 (2026)

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Received 24 Mar 2026 Revised 27 Jun 2026 Accepted 1 Jul 2026 Published 9 Jul 2026 License CC BY 4.0

Keywords: Fractional TMNNV equation; stochastic partial differential equation; noise-induced bifurcation; chaos; soliton; Lyapunov exponent; multistability; Caputo derivative.

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Umar, M. An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics. J. Comp. Math. Phy. 1, 11–27 (2026). http://jcmp.org/articles/2026-1-1-002

Umar, M. (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), 11–27. http://jcmp.org/articles/2026-1-1-002

Muhammad Umar. "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. 11–27, http://jcmp.org/articles/2026-1-1-002.

Muhammad Umar. "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): 11–27. http://jcmp.org/articles/2026-1-1-002.

Umar M. An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics. J. Comp. Math. Phy.. 2026;1(1):11-27. Available from: http://jcmp.org/articles/2026-1-1-002

@article{mar2026anuncertaintyaware,
  title = {An Uncertainty-Aware Physics-Informed Neural Network Framework for Nonlinear Fractional Partial Differential Equations in Mathematical Physics},
  author = {Umar, Muhammad},
  journal = {Journal of Computational Mathematics and Physics},
  year = {2026},
  volume = {1},
  number = {1},
  pages = {11--27},
  url = {http://jcmp.org/articles/2026-1-1-002},
}