An Algorithm for Fresnel Diffraction Computing Based on Fractional Fourier Transform

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

Inhomogeneous Fractional Diffusion Equations

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

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

MSC 2010: 35R11, 42A38, 26A33, 33E12

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

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

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

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

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

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

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

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

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

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05