A Fractional LC − RC Circuit

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.

α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

2000 Mathematics Subject Classification: 65M06, 65M12.

Backlund-Darboux Transformations in Sato's Grassmannian

We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Inhomogeneous Fractional Diffusion Equations

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05

Theorem for Series in Three-Parameter Mittag-Leffler Function

Mathematics Subject Classification 2010: 26A33, 33E12.

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.

Branching Particle Representation of a Class of Semilinear Equations

2000 Mathematics Subject Classification: 60J80, 60J85

Solvability of an Infinite System of Singular Integral Equations

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

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

Dunkl-Schrödinger Equations with and without Quadratic Potentials

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