@article{Zheng2025, 
author = {Jia Zheng and Xiuling Li and Yanni Pang and Hongying Wang and Tongchao Wang and Jiaxuan Sun},
title = {Continuous dependence and stability for a class of fractional partial differential equations with multiple parameters},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {27837-27861},
keywords = {fractional partial differential equations, variational methods, Lipschitz continuity, Gâteaux differentiability, dependence on parameters},
url = {https://www.sciopen.com/article/10.3934/math.20251223},
doi = {10.3934/math.20251223},
abstract = {In this paper, we studied the continuous dependence and stability of solutions for a class of fractional partial differential equations with multiple spatially varying coefficient parameters. The nonlocal operator was defined by a symmetric kernel, yielding a self-adjoint structure essential to the analysis. Using variational methods and the Minty–Browder theorem, we established the existence and uniqueness of weak solutions in the energy space        X    0   for each admissible parameter vector    w. We extended single-parameter stability to a multi-parameter framework by proving that the solution operator        S    f   is continuous with respect to    w in the product space        ∏    i        L                  q        i              (  Ω  ). Moreover, we derived an explicit global Lipschitz estimate for        S    f   and showed its Gâteaux differentiability under mild regularity assumptions on    f  (  x  ,  u  ,  w  ). Numerical simulations confirmed continuity, Lipschitz stability, and differentiability of        S    f   with respect to all parameters. These results provided rigorous guarantees for inverse problems and uncertainty quantification in multi-parameter fractional PDE models.}
}