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.

Covers modern topics in analysis and partial differential equations Fosters international collaboration Gives an overview of recent developments in modern problems and methods of mathematical physics and their applications

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**Ravshan Radjabovich Ashurov **is a professor of mathematics and the head of the Laboratory of Differential Equations and their Applications at the V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences. He earned his PhD in 1982 and his Doctor of Science in 1992, both from Moscow State University. His main area of interest is differential equations and mathematical physics. More specifically, he works on fractional differential equations, spectral theory of differential and pseudo-differential operators, harmonic analysis, and wavelet transforms. Throughout his career, he has collaborated with various international institutions, including the University of Birmingham, Vanderbilt University, and the International Centre for Theoretical Physics in Trieste. He has also contributed to academic conferences, such as the IX International Scientific Conference "Modern Problems of Applied Mathematics and Information Technologies – Al-Khwarizmi 2024" held in Tashkent, where he was a keynote speaker. With over 100 scientific publications, including books and monographs in multiple languages, he has significantly advanced the understanding of inverse problems in fractional differential equations and their applications.   Erkinjon Karimov is a post-doctoral researcher at the Ghent Analysis and PDE Center at Ghent University, Belgium. His main area of interest is in partial differential equations of integer and fractional order and special functions, connected with such PDEs, and direct and inverse problems for PDEs. He has published extensively in peer-reviewed journals, contributing to advancements in direct and inverse problems for fractional-order PDEs and mixed-type PDEs. His work has been cited widely, reflecting his impact on the scientific community. He holds a Ph.D. (2006) and D.Sc. (2020) from V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, where he focused on direct and inverse problems for PDEs of various types, including mixed-type. Throughout his career, he has collaborated with researchers from the University of Santiago de Compostela, the University of Las Palmas de Gran Canaria, Sultan Qaboos University, etc. His projects have been supported by the State Agency for Science and Technology of the Republic of Uzbekistan, ICMS (Great Britain), ICTP (Italy), and TWAS-CAS (China). In addition to his research, he is actively involved in teaching, mentoring, and managing scientific journals, demonstrating his commitment to education and the development of future scientists.

Inhalt

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.