What question did this study set out to answer?

The main aim is to explore the existence, uniqueness, and stability of solutions for a specific time-fractional equation.

January 25, 2026MathematicsOpen Access

On a Time-Fractional Biharmonic Nonlocal Initial Boundary-Value Problem with Frictional and Viscoelastic Damping Terms

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Research investigates solution existence and stability in a fractional partial differential equation, suggesting new analytical methods are needed.

The main aim is to explore the existence, uniqueness, and stability of solutions for a specific time-fractional equation.
Analyzed a fourth-order partial differential equation with initial and nonlocal boundary conditions.
Utilized Caputo fractional derivative and biharmonic operator in the formulation.
Developed a functional analytic framework using Sobolev spaces.
Employed energy estimates to establish well-posedness.
Demonstrated the existence and uniqueness of solutions under the specified conditions.
Proved stability of the solutions through rigorous mathematical analysis.

Alrajhi et al. (2026) studied this question.

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Research investigates solution existence and stability in a fractional partial differential equation, suggesting new analytical methods are needed.