*Correspondence: [email protected] School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P.R. China Abstract In this paper, we study some new retarded Volterra-Fredholm type integral inequalities on time scales, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as tools in the qualitative theory ...

In this paper, we present a numerical method to solve the nonlinear Volterra-Fredholm integral equations by new basis functions (NFs). This is demonstrated by using a complementary pair of new orthogonal basis functions set (NFs) derived from the well-known block pulse functions set. Finally, we give some numerical examples, and the efficiency of this method will be shown by comparison with som...

A numerical method based on modified block pulse functions is proposed for solving the mixed linear Volterra-Fredholm integral equations. We obtain an integration operational matrix of interval [0,T). and their integration, equations can be reduced to a system algebraic The rate convergence O(h) error analysis are discussed. Some examples provided show that have good degree accuracy.

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...

In this paper, a numerical procedure for solving a class of nonlinear VolterraFredholm integral equations is presented. The method is based upon the globally defined sinc basis functions. Properties of the sinc procedure are utilized to reduce the computation of the nonlinear integral equations to some algebraic equations. Illustrative examples are included to demonstrate the validity and appli...

In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science engineering. Nonlocal boundary conditions more effective, some cases necessary, because they accurate measurements of the true state than classical (local) initial conditions. Closed-form solutions always desirable, not only efficient, but also can be valuable benchmarks...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...