EXISTENCE RESULTS FOR SOME p-KIRCHHOFF PROBLEMS WITH ψ-HILFER FRACTIONAL DERIVATIVE

Hadeel Z. Alzumi, Wafa Shammakh () and Abdeljabbar Ghanmi ()
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Hadeel Z. Alzumi: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
Wafa Shammakh: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
Abdeljabbar Ghanmi: ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvédère, Tunis El Manar University, Tunis, Tunisia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-9

Abstract: In this paper, we investigate the existence of solutions to a p-Kirchhoff problem involving the ψ-Hilfer fractional derivative. Specifically, we reformulate the problem by analyzing the associated functional energy. We then construct three disjoint sets and demonstrate that the functional energy has a critical point in each of these sets. Finally, based on the definitions of these sets, we show that in the first set the solution is positive, in the second set the solution is negative, and in the third set, the solution changes sign.

Keywords: Fractional Calculus; Variational Methods; Existence of Solutions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400973

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