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

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

An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Mathematics Subject Classification: 44A40, 45B05

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

Time–Harmonic Behaviour of a Cracked Piezoelectric Solid by BIEM

ACM Computing Classification System (1998): J.2, G.1.9

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

α-Mellin Transform and One of Its Applications

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

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.

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

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

Inhomogeneous Fractional Diffusion Equations

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

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10