Version 1
: Received: 27 March 2024 / Approved: 27 March 2024 / Online: 27 March 2024 (13:38:19 CET)
How to cite:
Alzumi, H.Z.; Shammakh, W.; Ghanmi, A. Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative. Preprints2024, 2024031687. https://doi.org/10.20944/preprints202403.1687.v1
Alzumi, H.Z.; Shammakh, W.; Ghanmi, A. Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative. Preprints 2024, 2024031687. https://doi.org/10.20944/preprints202403.1687.v1
Alzumi, H.Z.; Shammakh, W.; Ghanmi, A. Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative. Preprints2024, 2024031687. https://doi.org/10.20944/preprints202403.1687.v1
APA Style
Alzumi, H.Z., Shammakh, W., & Ghanmi, A. (2024). Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative. Preprints. https://doi.org/10.20944/preprints202403.1687.v1
Chicago/Turabian Style
Alzumi, H.Z., Wafa Shammakh and Abdeljabbar Ghanmi. 2024 "Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative" Preprints. https://doi.org/10.20944/preprints202403.1687.v1
Abstract
In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.
Keywords
Fractional calculus; Variational methods; $\psi$-Hilfer operators, Existence of solution.
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
