Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

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

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

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

A Dichotomy for Ordinary Differential Equations in a Banach Space

A dichotomysimilar property for a class of homogeneous differential equations in an arbitrary Banach space is introduced. By help of them, existence of quasi bounded solutions of the appropriate nonhomogeneous equation is proved.

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo

On the 3-Wave Equations with Constant Boundary Conditions

2010 Mathematics Subject Classification: 37K40, 35Q15, 35Q51, 37K15.

Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations

2010 Mathematics Subject Classification: 34A30, 34A40, 34C10.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Anomalous Singularities for Hyperbolic Equations with Degeneracy of Infinite Order

2002 Mathematics Subject Classification: 35L80

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15

On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40

On Differential Inclusions with Unbounded Right-Hand Side

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

Dunkl-Schrödinger Equations with and without Quadratic Potentials

2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.