In this study, Chebyshev polynomials have been applied to construct an approximation method attain the solutions of linear fractional Fredholm integro-differential equations (IDEs). By method, IDE has transformed into a algebraic system with aid collocation points. conformable derivatives calculated in terms polynomials. Using results these calculations, matrix relation for was attained first t...

In this paper studies the exponential stability result is derived for second-order fractional stochastic integro-differential equations (FSIDEs) driven by sub-fractional Brownian motion (sub-fBm). By constructing a successive approximation method, we present pth moment of FSIDEs using analysis techniques and calculus (FC). At last, an example demonstrated to illustrate obtained theoretical resu...

A class of singular integro-differential equations in Lebesgue spaces are studied. There are many applications of the singular integro-differential equations discussed in this paper. An example in modeling the stress distribution of an elastic medium with holes is discussed in the paper. Direct numerical schemes using a collocation method and a mechanical quadrature rule designed for the singul...

Abstract: In this paper, Laplace decomposition method is developed to solve linear and nonlinear fractional integrodifferential equations. The proposed method is based on the application of Laplace transform to nonlinear fractional integro-differential equation. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivative is described in the Caputo se...