The Sumudu decomposition method was used and developed in this paper to find approximate solutions for a general form of fractional integro-differential equation Volterra Fredholm types. Caputo definition deal with derivatives. As the under consideration depends mainly on writing non-linear terms, which are often found inside kernel integral equation, it Adomian’s polynomials well-known way. Af...

Although perturbation techniques are widely applied to analyze nonlinear problems in science and engineering, they are however so strongly dependent on small parameters appeared in equations under consideration that they are restricted only to weakly nonlinear problems. For strongly nonlinear problems which don’t contain any small parameters, perturbation techniques are invalid. So, it seems ne...

In this paper, by using the theories and methods of integral equation and computer algebra, a reliable algorithm for solving the Volterra integral equation is established, and a new Maple algorithm mainproc is established, too. Some examples are presented to illustrate the implementations of the algorithm. The results of the examples indicate that the algorithm of Taylor polynomial method is si...

A new generalized Yosida inclusion problem, involving A-relaxed co-accretive mapping, is introduced. The resolvent and associated approximation operator construed a few of its characteristics are discussed. existence result quantified in q-uniformly smooth Banach spaces. four-step iterative scheme proposed convergence analysis Our theoretical assertions illustrated by numerical example. In addi...

In this paper we present a new approach for linear Volterra integral equations that is based on optimal control theory. Some optimal control problems corresponding Volterra integral equation be introduced which we solve these problems by discretization methods and linear programming approaches. Finally, some examples are given to show the efficiency of approach. Index Terms —Volterra integral e...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

recently, the block-pulse functions (bpfs) are used in solving electromagnetic scattering problem, which are modeled as linear fredholm integral equations (fies) of the second kind. but the theoretical aspect of this method has not fully investigated yet. in this article, in addition to presenting a new approach for solving fie of the second kind, the theory of both methods is investigated as a...

in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...