in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.

We study the thermoelastic deformation of an elastic layer. The upper surface of the medium is subjected to a uniform thermal field along a circular area while the layer is resting on a rigid smooth circular base. The doubly mixed boundary value problem is reduced to a pair of systems of dual integral equations. The both system of the heat conduction and the mechanical problems are calculated b...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...

‎‎‎in this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear volterra integral equations (2d-nvies) of the first kind‎. ‎here‎, ‎we convert a 2d-nvie of the first kind to a one-dimensional linear vie of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎we also verify convergence and error analysis of the method‎. ‎at t...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...