Funding: This work was supported by the National Natural Science Foundation of China (11471015 and 12301185), the Natural Science Research Projects of Higher Education Institutions in Anhui Province (2024AH050080), the Postdoctoral Scientific Research Project for Anhui Jianzhu University (2024QDHZ04), and the China Postdoctoral Science Foundation-Anhui Joint Support Program (2024T006AH).

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ABSTRACT

In this paper, we study a class of nonlinear space–time fractional Kirchhoff-type diffusion equations when the external force contains hereditary characteristics involving bounded and unbounded delays. Firstly, the well-posedness of the problem is analyzed in phase space ${\mathbf{C}}_{\rho}\left(\cdotp \right)$ by using the Galerkin method and energy estimations. Furthermore, based on a corollary of the Brouwer fixed point theorem, the existence and uniqueness of the stationary solution of the problem are established. In addition, we also discuss the stability of the unique stationary solution.

Conflicts of Interest

The authors declare no conflicts of interest.

Open Research

Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Volume48, Issue12

August 2025

Pages 12048-12067

A Class of Nonlinear Space–Time Fractional Kirchhoff-Type Diffusion Equations With Delay

ABSTRACT

Conflicts of Interest

Open Research

Data Availability Statement

References

References

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A Class of Nonlinear Space–Time Fractional Kirchhoff-Type Diffusion Equations With Delay

ABSTRACT

Conflicts of Interest

Open Research

Data Availability Statement

References

References

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