Fuzzy Backstepping Approach to Stabilizing Fuzzy Parabolic Partial Differential Equations

Authors

Zainab John, School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Malaysia AND Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Fadhel S. Fadhel, Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadira, Baghdad, IraqFollow
Samsul Ariffin Abdul Karim, Institute of Strategic Industrial Decision Modelling (ISIDM), School of Quantitative Sciences, UUM College of Arts and Sciences, Universiti Utara Malaysia, 06010 Sintok, Malaysia AND Computational Statistics and Applied Mathematics (CSAM) Research Group, School of Quantitative Sciences, UUM College of Arts and Sciences, Universiti Utara Malaysia, 06010 Sintok, Malaysia
Teh Yuan Ying, School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Malaysia

Abstract

In this work, we study the solvability and stability of the fuzzy reaction-diffusion equation and the fuzzy diffusion equation with nonhomogeneous boundary conditions. Firstly, we derive the fuzzy exact solutions by converting the nonhomogeneous boundary condition to a homogeneous condition, then we prove the instability of the solution by using simulation approach with the help of Maple program. From this, we have decided to implement the fuzzy backstepping approach to developed the stabilization of the fuzzy parabolic partial differential equations. By using this approach together with the generalized Hukuhara (gH) derivative, we were able to find the control solution for the unstable equations and prove the stability of the fuzzy control solutions through simulation.

Recommended Citation

John, Zainab; Fadhel, Fadhel S.; Karim, Samsul Ariffin Abdul; and Ying, Teh Yuan (2025) "Fuzzy Backstepping Approach to Stabilizing Fuzzy Parabolic Partial Differential Equations," Iraqi Journal for Computer Science and Mathematics: Vol. 6: Iss. 4, Article 13.
DOI: https://doi.org/10.52866/2788-7421.1338
Available at: https://ijcsm.researchcommons.org/ijcsm/vol6/iss4/13