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...

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...

First, we develop a direct operator method for solving boundary value problems class of nth order linear Volterra–Fredholm integro-differential equations convolution type. The proposed technique is based on the assumption that Volterra bijective and its inverse known in closed form. Existence uniqueness criteria are established exact solution derived. We then apply this to construct form fourth...

In this paper, we present some new GronwallBellmann type discrete fractional sum inequalities, and based on them present some Volterra-Fredholm type discrete inequalities. These inequalities are of new forms compared with the existing results in the literature, and can be used in the research of boundedness and continuous dependence on the initial value for solutions of fractional difference eq...

Infinite horizon backward stochastic Volterra integral equations (BSVIEs for short) are investigated. We prove the existence and uniqueness of adapted M-solution in a weighted $L^2$-space. Furthermore, we extend some important known results finite BSVIEs to infinite setting. provide variation constant formula class linear duality principle between (forward) equation (SVIE an BSVIE As applicatio...