On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

Rétractes Absolus de Voisinage Algébriques

2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.

Comparative Analysis of the Opposite Rotating Cylinders Impact over Couette Flow for Rarefied Gas

Петър Господинов, Добри Данков, Владимир Русинов, Стефан Стефанов - Иследвано е цилиндрично течение на Кует на разреден газ в случая на въртене на два коаксиални цилиндъра с еднакви по големина скорости, но в различни посоки. Целта на изследването е да се установи влиянието на малки скорости на въртене върху макрохарактеристиките – ρ, V , . Числените резултати са получени чрез използване на DSMC и числено решение на уравненията на Навие-Стокс за относително малки (дозвукови) скорости на въртене. Установено е добро съвпадение на резултатите получени по двата метода за Kn = 0.02. Установено е, че съществува “стационарна” точка за плътността и скоростта. Получените резултати са важни при решаването на неравнини, задачи от микрофлуидиката с отчитане на ефектите на кривината. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.

Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.

On Differential Inclusions with Unbounded Right-Hand Side

2000 Mathematics Subject Classification: 58C06, 47H10, 34A60.