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

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

On the Generalized Confluent Hypergeometric Function and Its Application

2000 Mathematics Subject Classification: 26A33, 33C20

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

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

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

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

On the Generalized Associated Legendre Functions

Mathematics Subject Classification: 33C60, 33C20, 44A15

On the Mastering of Knowledge and Skills for Solving Mathematical Problems in the Context of the Relationship "Reflection–Synergy"

On the basis of topical investigations on the reflection in the mathematics education, in this article there are presented some contemporary ideas about refining the methodology of mastering knowledge and skills for solving mathematical problems. The thesis is developed that for the general logical and for some particular mathematical methods to become means of solving mathematical problems, first they need to be a purpose of the education.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

On the Mathematical Modelling of Microbial Growth: Some Computational Aspects

We propose a new approach to the mathematical modelling of microbial growth. Our approach differs from familiar Monod type models by considering two phases in the physiological states of the microorganisms and makes use of basic relations from enzyme kinetics. Such an approach may be useful in the modelling and control of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme inhibitory conditions. Some computational experiments are performed in support of our modelling approach.

On the Operational Solution of a System of Fractional Differential Equations

MSC 2010: 26A33, 44A45, 44A40, 65J10

On the Quotient Function Employed in the Blind Source Separation Problem

MSC 2010: 42C40, 94A12