What question did this study set out to answer?

The research aims to analyze impulsive boundary value problems involving Hilfer fractional derivatives and the p-Laplacian operator, focusing on solution multiplicity and stability.

August 7, 2026AxiomsOpen Access

Analytical Study of Impulsive Hilfer-Type Fractional p-Laplacian Problems Using Neural Networks and Finite-Difference Methods

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Authors

RKRahman Ullah KhanQuaid-i-Azam University IAIoannis K. ArgyrosCameron University TRTaha RadwanQassim University

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Implication

Analytical study explores solutions and stability in impulsive fractional p-Laplacian problems with neural networks and finite differences.

Key Points

The research aims to analyze impulsive boundary value problems involving Hilfer fractional derivatives and the p-Laplacian operator, focusing on solution multiplicity and stability.
Constructed variational functional by incorporating point-impulse contributions and using Hilfer fractional derivatives.
Proved existence of weak solutions using the fountain theorem and conducted stability analysis based on weak residuals.
Developed neural surrogate models incorporating boundary constraints via finite-difference methods.
Demonstrated the existence of two sequences of weak solutions: one of unbounded energy and another tending to zero.
Achieved local generalized Hyers-Ulam stability estimates under the given assumptions and stability analysis framework.
Illustrated convergence behavior and examined the impact of Hilfer-type parameters on solutions.

Cite This Study

Khan et al. (2026) studied this question.

synapsesocial.com/papers/6a758be1847ab6d26c01f7fa https://doi.org/10.3390/axioms15080591

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Implication

Analytical study explores solutions and stability in impulsive fractional p-Laplacian problems with neural networks and finite differences.

Analytical Study of Impulsive Hilfer-Type Fractional p-Laplacian Problems Using Neural Networks and Finite-Difference Methods

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Implication

Key Points

Cite This Study

Analytical Study of Impulsive Hilfer-Type Fractional p-Laplacian Problems Using Neural Networks and Finite-Difference Methods

Discussion

Member takes

Implication

Key Points

Cite This Study

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