This book convenes peer-reviewed, selected papers presented at the Tenth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Saints Constantine and Helena, Bulgaria, July 1720, 2023. Contributions are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.

In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them to solve real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.

Provides solutions to industrial problems with a focus on real-world applications Presents many computer simulations Includes wide range of applications in fields like physics, biology, economics, and neuroscience

Autorentext

Angela Slavova obtained her Master's degree in Computer Science (1986) and her PhD in Mathematics (1994) from the University of Ruse, Bulgaria. In 2005, she became a Doctor of Science and, in 2007, a Full Professor at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences. Since 2004, Prof. Slavova is Head of the Department of Mathematical Physics, Institute of Mathematics, Bulgarian Academy of Sciences, and, since 2011, Head of the Department of Differential Equations and Mathematical Physics at the same Institute. Her research work focuses on the field of differential equations; cellular nonlinear and nanoscale networks; nonlinear waves propagation; equations of mathematical physics; and applications of differential equations in sciences.

Inhalt

Part I: 1.2-d minimal surface ow with the oblique condition and translators(L. Ma and Y. Pan).- 2. Graphical portraits of the solutions of binary first order nonlinear ordinary differential equation near their singular point(P. Popivanov and A. Slavova).- 3. Physics informed cellular neural networks for solving partial differential equations(A. Slavova and E. Litsyn).- 4. Several Relationships Connected to a Special Function used in the Simple Equations Method(SEsM)( N.K. Vitanov).- 5. On the Exact Solutions of a Sequence of Nonlinear Differential Equations Possessing Polynomial Nonlinearities(Z.I. Dimitrova).- 6. Improved Hardy inequality with logarithmic term(N. Kutev and T. Rangelov).-7. Robin boundary value problem for some nonlinear nonlocal elliptic partial differentialEquations(P. Popivanov and A. Slavova).-8. The Ericksen-Leslie System for Data on a Plane(D. Barbera and V. Georgiev).- 9. High frequency weighted resolvent estimates for the Dirichlet Laplacian in the exterior domain(V. Georgiev and M. Rastrelli).- 10. Influence of stimulus on the motion of substance in a channel of network(Z.I. Dimitrova, Y. Chorbadzhiyska Stamenova).- 11. Klein-Gordon equation with critical initial energy and nonlinearities with variable Coefficients(N. Kutev, M. Dimova and N. Kolkovska).- 12. Definite / indefinite integrals involving non-integral powers for certain trigonometric functions times special functions(Y. Mochimaru).- 13. A dynamic Green's function for the homogeneous viscoelastic and isotropic half-space(T.V. Rangelov, P.S. Dineva, and G.D. Manolis).- 14. Area and perimeter full distribution functions for planar Poisson line processes and Voronoi diagrams(A. Kanel-Belov, M. Golafshan, S. Malev, and R. Yavich).- 15. An Application of the Simplest Equations Method to Logarithmic Schrodinger Equation(Ivan P. Jordanov).- 16. Explicit solutions of the nonlinear Schrodinger-type equation(A. Syzdykova and G. Kudaibergenov).- 17. Didactic Approachto Study Mass Inertial Characteristics of Bodies in Plane Motion (V. Kotev, R. Rusinov, M. Rimeh, G. Ivanov, M. Ivanova, I. Jordanov).- 18. On the Loss of Regularity in a Degenerate Vibrating Beam Equation(P. Popivanov and B. Yordanov).- Part II: 19. Mittag - Le_er stability for non-instantaneous impulsive generalized proportional Caputo fractional di_erential equations(S. Hristova).- 20. Uniqueness Functions to Conformable Di_erential Inclusions(T. Donchev, J. Abbas, I. Nikolova, S. Stoilova).- 21. Numerous exact solutions of the Wu-Zhang system with conformable timefractional derivatives via Simple Equations Method (SEsM): The Case of Two Simple Equations(E.V. Nikolova).- 22. Impulses in generalized proportional Caputo fractional di_erential equations and equivalent integral presentation(S. Hristova and R. Terzieva).- 23. Reconstruction of the Time-Dependent Diffusion Coefficient in a Space-Fractional Parabolic Equation(M.N. Koleva and L.G. Vulkov).- 24. On the traveling wave solutions of the fractional diffusive predator prey system incorporating an Allee effect(E.V. Nikolova).- 25. Several exact solutions of the fractional predator prey model via the Simple Equations Method(SEsM) (R.G. Nikolov, E.V. Nikolova and V.N. Boutchaktchiev).- Part III: 26. Comparison Between the Chain Ladder Method and the Bornhuetter-Ferguson Method for Third Party Liability Insurance(E. Raeva and V. Pavlov and H. Redzheb) 27. Iterative Calibration of Implied Volatility for European Options: A Computational Approach (T. Klimenko and V. Pavlov).- 28. Mixed Approach between Capital Asset Pricing Model and ARIMA Model for Estimating the Standard and Poor's Stocks(E. Raeva and I. Raeva and Y. Ivanova).- 29. Measuring of Inferred Loss Rate with Application to Capital Adequacy(V. Boutchaktchiev).- 30. Comparative Analysis on Neural Networks and ARIMA for Forecasting Heterogeneous Portfolio Returns(A. Klimenko, V. Mihova, S. Georgiev, I. Georgiev and V. Pavlov).- 31.Some modifications of the Kies distribution Applications(N. Kyurkchiev, T. Zaevski, A. Iliev, and Asen Rahnev).- 32. Portfolio Construction Using Neural Networks and Multiobjective Optimization(T. Tsonev, S. Georgiev, I. Georgiev, V. Mihova and V. Pavlov).- 33. Advanced stochastic Monte Carlo optimization methods for two-dimensional European style options(V.Todorov and Slavi Georgiev).- 34.Simple Equations Method (SEsM): Exact Solutions for Description of COVID-19 Epidemic Waves (N.K. Vitanov).- 35. Numerical determination of age-dependent coefficients in an integro-hyperbolic system of honeybee population dynamics(S. Georgiev and L. Vulkov).- 36. Edge of chaos in reaction-diffusion system with memristor synapses (A. Slavova and V. Ignatov).- 37. Inverse Modelling of the Cellular Immune Response to SARS-CoV-2(S. Georgiev).- 38. Reconstruction of Boundary Conditions of a Parabolic-Hyperbolic Transmission Problem (M.N. Koleva and L.G. Vulkov).- 39. Novel Monte Carlo algorithmfor linear algebraic systems(V. Todorov, S. Georgiev, and I. Dimov).- 40. A note on the Hwang-Kim's universal activation function(M. Vasileva and N. Kyurkchiev).- 41. Special lattice and digital sequences for multidimensional air pollution modelling (V. Todorov, S. Georgiev, and I. Dimov).- 42. Some applications of the Dickson polynomials of higher kind for modeling radiation diagrams (M. Vasileva, V. Kyurkchiev, A. Iliev, A. Rahnev and N. Kyurkchiev).- 43. Novel stochastic method for multidimensional Fredholm integral equations(V. Todorov, S. Georgiev, and Y. Dimitrov).