Article · Uzbek Mathematical Journal · September 5, 2025
A Four-Parameter non-local Problem for a Fractional Wave Equation
Ravshan Ashurov, Navbahor Nuraliyeva
Abstract
In this paper, we investigate a time-fractional diffusion-wave equation, where the classi- cal second-order time derivative is replaced by a fractional derivative of order ρ ∈ (1, 2). We consider a class of non-local boundary value problems involving four real parameters α1, α2, β1, and β2 under general conditions. Using the Fourier method in an abstract Hilbert space setting, we derive necessary and sufficient conditions for the well-posedness of the problem. We prove that the solution exists and is unique if certain algebraic conditions on the parameters are satisfied. In cases where these conditions fail, we describe the structure of the solution and show that uniqueness may be lost. For such cases, we also formulate orthogonality conditions that guarantee existence.
More by Navbahor Nuraliyeva
- MIXED-TYPE EQUATION WITH THE CAPUTO FRACTIONAL DERIVATIVE AND THE DEZIN-TYPE NON-LOCAL CONDITION ON THE TORUSJournal of Mathematical Sciences · 2026
- Nonlocal Problem with Parameters for a Caputo Fractional-Order EquationTrends in mathematics · 2026
- Forward and inverse problems for a mixed-type equation with the Caputo fractional derivative and Dezin-type non-local conditionBULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS · 2025 · Citations: 1
- A Nonlinear Nonlocal Problem for the Caputo Fractional Subdiffusion EquationarXiv · 2025