The Stein-Weiss Type Inequality for Fractional Integrals, Associated with the Laplace-Bessel Differential Operator

2000 Math. Subject Classification: Primary 42B20, 42B25, 42B35

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

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

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

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

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

Mathematics Subject Classification: 26A33

Conditional probability calculations for the nonlinear Schrödinger equation with additive noise

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33

Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

Mathematics Subject Classification: 26A33, 93B51, 93C95

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

A Brief Story about the Operators of the Generalized Fractional Calculus

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

Fractional Integration and Fractional Differentiation of the M-Series

Mathematics Subject Classification: 26A33, 33C60, 44A15

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