On the Generalized Confluent Hypergeometric Function and Its Application

2000 Mathematics Subject Classification: 26A33, 33C20

Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

2000 Mathematics Subject Classification: 26A33, 33C45

Generalized Discernibility Function Based Attribute Reduction in Incomplete Decision Systems

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditional attributes. Our methods use generalized discernibility matrix and function in tolerance-based rough sets.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.

On the Generalized Associated Legendre Functions

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

Further Generalization of Kobayashi's Gamma Function

In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

A Brief Story about the Operators of the Generalized Fractional Calculus

2000 Mathematics Subject Classification: 26A33, 33C60, 44A20

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.

Fractional Integration of the Product of Bessel Functions of the First Kind

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99