10.57647/j.jtap.2025.1901.09

Identification of unknown source term in space and time fractional Fokker-Planck equations

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  • Amir Hossein Salehi Shayegan*1,
  • Laya Dejam2,
  1. Mathematics Department, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran  AND  Quantum Technologies Research Center (QTRC), Science and Research Branch, Islamic Azad University, Tehran, Iran
  2. Quantum Technologies Research Center (QTRC), Science and Research Branch, Islamic Azad University, Tehran, Iran AND Physics Department, West Tehran Branch, Islamic Azad University, Tehran, Iran

Received: 2024-10-21

Revised: 2024-12-23

Accepted: 2025-01-07

Published 2025-02-10

Copyright (c) 2025 Amir Hossein Salehi Shayegan, Laya Dejam (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Salehi Shayegan AH, Dejam L. Identification of unknown source term in space and time fractional Fokker-Planck equations. J Theor Appl phys. 2025 Feb. 10;19(01):1-10. Available from: https://oiccpress.com/jtap/article/view/8605
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Abstract

The problem of identifying the source term in space and time fractional Fokker-Planck equations is considered. Due to this, a methodology based on the quasi solution approach is applied and it is proved that the Fréchet derivative of the suggested cost functional may be expressed through the solution of an adjoint problem. Furthermore, we demonstrate the Lipschitz continuity of the gradient. With these results, it is possible to establish the existence and uniqueness of a quasi solution and construct a monotone iteration scheme using a gradient-type method. Finally, the convexity of the Fréchet derivative is provided.

Keywords

  • Fractional Fokker-Planck equations,
  • Quasi-solution,
  • Computational algorithm,
  • Regularization
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