Abstract In this paper, the numerical method for solving Abel’s integral equations is presented. This method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply fractional properties for solving Abel’s integral equations of the first and second kind. The fractional operator is considered in the sense of RiemannLiouville. Although Abel’s integral equations as singu...

In the paper stochastic Volterra equations of nonscalar type are studied using resolvent approach. The aim of this note is to provide some results on stochastic convolution and integral mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials.

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

Homotopy perturbation method is a well-known method for solving many functional equations such as differential equations, integral equations, integro-differential equations and so on. Applying this method needs some computations which are boring by hand. Therefore, creating a program to do all computations would be useful. In this work, a maple program is prepared to solve the second kind of Vo...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...