### On Treating of Surface Cracks in Finite Layers of Fractional Materials

Hassan Khayyat

#### Abstract

The plane strain problems of the bounded layer medium composed of three different materials contain a crack on one of the interface are considered. Using Fourier integral transform, the boundary value problem leads to a mixed integral equation with Cauchy kernel in position and continuous kernel in time. In addition, using a quadratic numerical method we have a system of Fredholm integral equations with Cauchy kernel in position.   Then, the Jacobi polynomials method, according to the index of integral equation, is used to solve the system of Fredholm integral equations. Moreover, the developing program is used to computing the approximate solution and the estimated error.

#### Keywords

Fracture mechanics; Fourier integral transform; System of Fredholm integral equations; Cauchy kernel; Jacobi polynomial.

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