What does this research mean for the field?

Weak solutions for nonlinear boundary value problems driven by a ψ-Hilfer fractional p-Laplacian operator exist and can be infinitely multiple for all fractional orders α ∈ (0, 1), overcoming previous restrictions that required α > 1/p. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish the existence and multiplicity of weak solutions for nonlinear boundary value problems driven by a psi-Hilfer fractional p-Laplacian operator across the full parameter interval.

September 3, 2026Asian-European Journal of Mathematics

On a ψ-Hilfer fractional p -Laplacian differential equation: Existence and multiplicity results

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Authors

WAWael AbdelhediUniversity of Sfax HCHichem ChtiouiUniversity of Sfax

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Implication

Variational analysis demonstrates the existence and multiplicity of weak solutions in fractional p-Laplacian systems, unifying several classical fractional derivative frameworks.

Key Points

To establish the existence and multiplicity of weak solutions for nonlinear boundary value problems driven by a psi-Hilfer fractional p-Laplacian operator across the full parameter interval.
Constructed a variational framework within an appropriate fractional derivative Banach space.
Proved a refined compact embedding theorem valid for all order parameters in the unit interval without traditional restrictive bounds.
Applied critical point theory, the Mountain Pass Theorem under Ambrosetti-Rabinowitz conditions, and Krasnoselskii's genus theory.
Demonstrated the existence of at least one weak solution under sub-linear growth conditions.
Established the existence of nontrivial solutions under super-linear conditions and infinitely many solutions for symmetric nonlinearities.
Unified Riemann-Liouville, Caputo, and Hadamard fractional formulations under a single analytical framework.

Cite This Study

Abdelhedi et al. (2026) studied this question.

synapsesocial.com/papers/6a993626636c6408cfa7eefa https://doi.org/10.1142/s179355712650107x

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September 3, 2026Asian-European Journal of Mathematics

On a ψ-Hilfer fractional p -Laplacian differential equation: Existence and multiplicity results

View Full Paper

Ask AI

Bookmark

Authors

WAWael AbdelhediUniversity of Sfax HCHichem ChtiouiUniversity of Sfax

Discussion

Member takes

Implication

Variational analysis demonstrates the existence and multiplicity of weak solutions in fractional p-Laplacian systems, unifying several classical fractional derivative frameworks.

Key Points

To establish the existence and multiplicity of weak solutions for nonlinear boundary value problems driven by a psi-Hilfer fractional p-Laplacian operator across the full parameter interval.
Constructed a variational framework within an appropriate fractional derivative Banach space.
Proved a refined compact embedding theorem valid for all order parameters in the unit interval without traditional restrictive bounds.
Applied critical point theory, the Mountain Pass Theorem under Ambrosetti-Rabinowitz conditions, and Krasnoselskii's genus theory.
Demonstrated the existence of at least one weak solution under sub-linear growth conditions.
Established the existence of nontrivial solutions under super-linear conditions and infinitely many solutions for symmetric nonlinearities.
Unified Riemann-Liouville, Caputo, and Hadamard fractional formulations under a single analytical framework.

Cite This Study

Abdelhedi et al. (2026) studied this question.

synapsesocial.com/papers/6a993626636c6408cfa7eefa https://doi.org/10.1142/s179355712650107x

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