2024/03/18 by Ravshan Ashurov, Ashurov, Ravshan, Muhiddinova, Oqila
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2403.11638
openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the equation does not depend on the solution of the problem and 2) it depends on the solution, but at the same time satisfies the classical Lipschitz condition with respect to this variable and an additional condition which guarantees a global existence of the solution. Sufficient conditions are found (in some cases they are necessary) on the initial function and on the right-hand side of the equation, which ensure the existence of a classical solution. In previously known works, linear but more general systems of fractional pseudodifferential equations were considered and the existence of a weak solution was proven in the special classes of distributions.