New Trends in the Applications of Differential Equations in Sciences

Part1.Applications in Mathematical Physics.- Ground states of Schrödinger-Poisson-Slater equations with linear non-local terms.- Interpolation of Sobolev spaces for Laplace operator with contact interaction.-Exact travelling wave solutions to several fully nonlinear PDE and radial solutions of boundary value problem to the Liouville equation in circular domains in the plane.- Recent developments in the methodology of the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear differential equations.- Forward stability conditions and applications.- Exact solutions of the Troesch's problem.- Pavlina Atanasova, Valentin Georgiev, On the special cases of the Jacobi elliptic function solutions of the (2+1)-dimensional Sine-Gordon equation.- An application of the method of simplest equation for exact real solutions of the model for spatial - time interaction of populations.- A characterization of the K-functional for the algebraic version of the trigonometric Jackson integrals Gs,n in generalized weighted integral metric.- Mixed semicontinuous fully nonlinear evolution inclusions.- Nonlinear waves in the diffusion-advection-reaction model of interacting populations incorporating nonlocal effects and long range diffusion.- Physic informed neural networks for solving nonstandard initial-boundary value problem for second order hyperbolic equation.- Approximate solution of the optimal control problem with the Hukuhara derivative equation with rapidly fluctuating coefficients on a finite interval.- Travelling wave solutions of the Wu-Zhang system of PDE.- Physics informed neural networks for solving predator-prey models.- Part2. Applications in Mechanics.- On nonlinear waves in microtubules generated by means of a linear simple equation.- On a mathematical model describing pollution processes in a channel.- On nonlinear waves in microtubules generated by means of simple equation of Bernoulli kind.- Analysis of non-periodic buckling in an axisymmetric thin uniform shell.- On nonlinear waves in microtubules.- An education facility for design and mathematical modeling of 4 bar linkage mechanism.- Part3. Applications in Numerical Methods and Computer Science.- An improved interpolation error estimate from a new Taylor-like formula: Application to finite element method.- Mixed finite element method applied to sixth-order eigenvalue problem.- Advanced unbiased Monte Carlo for multidimensional Fredholm integral equations.- Novel stochastic sequences for multidimensional air pollution modelling.- Advanced stochastic method for linear algebraic systems.- Stochastic approaches for the mutidimensional Volterra integral equation.- Numerical analysis of a difference scheme family for solving semilinear hyperbolic PDEs.- Numerical solution of switched systems with delay.- Part4. Applications in Financial Mathematics.- Multicriteria optimization approach for investment project financing evaluation and decision making.- Application of weighted t-tests for loss-given-default forecasts validation.- A comparison of deep neural network and convolutional neural network for credit card fraud detection.- Studying the dependency between household income and consumption of basic food commodities in Bulgaria.- Accurate lattice-based models for pricing European options.- Advanced Monte Carlo optimizations for multidimensional European style options.- Part5. Applications in Mathematical Biology.- Comparison of exact solutions of model equations connected to the SIS and SIR model of epidemics spread.- Comparison of exact solutions of model equations connected to the SIR and SEIR model of epidemic spread.- Part6. Applications in Fractional Analysis.- Ulam type stability of Volterra fractional integral equations of variable-order.- Exact solitary wave solutions of the time-fractional fifth-order KdV-type equation via extended Simple Equations Method(SEsM).- Existence for a nonlinear boundary value problem for Riemann-Liouville fractional differential equations of variable order.