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.
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.
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.
