What question did this study set out to answer?

This research aims to explore the existence and long-term behavior of solutions to a fractional wave equation with nonlocal nonlinearity.

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February 17, 2026

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Key Points

This research aims to explore the existence and long-term behavior of solutions to a fractional wave equation with nonlocal nonlinearity.
Derived norm estimates for solutions
Analyzed long time behavior of solutions
Obtained local in time weak solutions
Developed global solutions with nonlocal non-power nonlinear terms
Confirmed the global existence of solutions
Described long time behavior of solutions
Established local weak solutions under specific conditions
Showed implications of nonlocal nonlinearity on solution behavior

Abstract

ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of which we derive particularly to observe the roles of and in the long time behavior of solutions. Moreover, we apply these estimates to obtain local in time weak solutions, and global solutions, under the influence of a nonlocal non‐power nonlinear term.

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Authors

Ibrahim Ahmad Suleman

Mokhtar Kirane

Journals

Mathematical Methods in the Applied Sciences

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Institutions

Khalifa University of Science and Technology

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Cite this study

Suleman et al. (Sun,) studied this question.

synapsesocial.com/papers/699405bb4e9c9e835dfd69c5 — DOI: https://doi.org/10.1002/mma.70575

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Nonlinear wave mechanics· 1976 · 757 citations
The fractional Laplacian as a limiting case of a self-similar spring model and applications to n-dimensional anomalous diffusion· 2013 · 25 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

An equation whose Fujita critical exponent is not given by scaling· 2006 · 94 citations
A Survey of Useful Inequalities in Fractional Calculus· 2017 · 46 citations
On the Asymptotic Behavior of Solutions of Semi-linear Wave Equations· 1976 · 390 citations
Nonlinear wave mechanics· 1976 · 757 citations
The fractional Laplacian as a limiting case of a self-similar spring model and applications to n-dimensional anomalous diffusion· 2013 · 25 citations

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study

Also consider

Also consider