Modern Methods in Mathematical Physics and their Applications
Description
This volume is a collection of selected peer-reviewed scientific results presented at the conference "Modern Methods in Mathematical Physics and their Applications" held in Uzbekistan from April 22 to 24, 2025. The aim of the conference was to exchange ideas as well as foster international collaboration. The main topics include algebra and analysis, direct and inverse problems for differential equations (both integer and fractional-order), spectral theory of differential operators, mathematical modeling, and computational mathematics. The book will be of interest to researchers working in these fields.
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Part I. Algebra and Analysis.- Chapter 1. Local and 2-local anti-derivations on the perfect Lie algebras Lm.- Chapter 2. Estimates for convolution operators related to sufficiently smooth surfaces.- Chapter 3. About asymptotic Critical Reduced Processes with Infinite Variance.- Chapter 4. Equivalence of Paths with Respect to the Action of the Group SO¹2` + 1;Rº.- Chapter 5. On the summability of the Fourier Laplace series of the distributions.- Chapter 6. Mixed Hessians in the class of m-convex functions.- Chapter 7. Invariants of pairs of anti-commuting matrices under simultaneous conjugation.- Part II. Differential Equations.- Chapter 8. On solutions of the Weyl fractional differential equation in Gevrey classes.- Chapter 9. Well-Posedness of the NBVP for Elliptic Equations.- Chapter 10. A nonlocal problem for hyperbolic systems with impulsive discrete memory: method and solution.- Chapter 11. Inverse Coefficient Problems for Mixed Parabolic-Hyperbolic equations.- Chapter 12. Study of mixed-type partial differential equations with Gerasimov-Caputo fractional derivatives: Forward and Inverse Problems.- Chapter 13. On a coefficient inverse problem for the three-dimensional Tricomi equation in a parallelepiped.- Chapter 14. Applications of Appell and Lauricella functions to solving the boundary value problems for the degenerate elliptic equation.- Chapter 15. Inverse Problem For A System Of Mixed-Type Second-Order Differential Equations.- Chapter 16. The direct and inverse problems for the fractional equation with the Hilfer derivative.- Chapter 17. Pseudo-differential equations in a plane with an angular cut.- Chapter 18. Forward and Inverse problem for the Langevin-type fractional equation.- Chapter 19. Samarskii - Ionkin type problem for a degenerate elliptic equation with a singular coefficient.- Chapter 20. Some boundary value problems for the triharmonic equation in a ball.- Chapter 21. Linear Inverse Coefficient Problems for Degenerate Elliptic Equations.- Chapter 22. Bitsadze-Samarskii problem for a mixed-type equation.- Chapter 23. On systems of fractional nonlinear partial differential equations.- Chapter 24. Nonlocal problem with parameters for a Caputo fractional-order equation.- Chapter 25. Nonlocal approach to Protter-Morawetz BVP for the 3-D Tricomi equation.- Chapter 26. Order Determination Inverse Problem for Fractional Diffusion-Wave Equation.- Chapter 27. Nonlocal problems for a degenerate equation and an equation of mixed type.- Chapter 28. Existence and uniqueness of a time-dependent coefficient and source problem for fractional telegraph equation.- Chapter 29. The time-independent source identification problem for the subdiffusion equation with the integral over-determination condition.- Chapter 30. Boundary value problem for space-time fractional diffusion equation on metric graphs.- Chapter 31. Nonlocal Riemann Problem.- Chapter 32. Fractional parabolic systems of vector order with Riemann-Liouville fractional derivative.- Chapter 33. Classical and weak solutions to the mixed problem for the time-fractional space degenerate partial differential equation.- Chapter 34. Mixed problems with integral conditions for a loaded pseudoparabolic equation of the third order.- Part III. Mathematical Modeling and Computational Mathematics.- Chapter 35. Investigation of dynamic modes of the FitzHugh-Nagumo oscillator with variable memory and external stimulus function.- Chapter 36. On the Time-Optimal Problem for a Heat Equation.- Chapter 37. Fractional Calculus for Design of Rock Tunnels.- Chapter 38. On some inverse problems of recovering the heat flux and the heat transfer coefficient from integral data.- Chapter 39. SDEs driven by CTRW-limit processes and associated FPK equations.