Study of the normality and continuity for the mixed integral equations with phase-lag term

Abstract

In this paper, the existence and uniqueness solution of the Fredholm-Volterra integral equations (F-VIEs) are considered in the space L 2 [0, 1]× C n [0, T ], 0 ≤ T < 1. Using a numerical technique, F-VIEs lead to a system of linear Fredholm integral equations (SLFIEs). Also, the normality and the continuity of integral operator are discussed. The Trapezoidal Rule is used to get the solution of SLFIEs. Finally, numerical results are discussed and the error estimate is computed.

Application of Adomian polynomials for solving nonlinear integro-differential equations

“…Many of these equations have already been studied in earlier papers on related topics. Among them, the equations with a weakly singular kernel in the network studies [10,21], in the non-linear Fredholm form [4,31], in the COVID-19 researches [29], in the non-linear Volterra-Fredholm form [28,32], in the non-linear Volterra form [16,17,30], in the linear Fredholm form [2,19,27], and others.…”

A novel iterative scheme for solving delay differential equations and nonlinear integral equations in Banach spaces

“…The demonstrative examples of such models can be found in the literature (see, for example, literature 16,17 ). Several problems in applied sciences are often reduced to Volterra‐Fredholm integral equations (see, for example, previous studies 18,19 and the references therein).…”

On a discussion of Volterra–Fredholm integral equation with discontinuous kernel

“…The illustrative examples of such models can be found in the literature (see, e.g., [1][2][3][4][5][6][7][8]). Many problems of mathematical physics, applied mathematics, and engineering are reduced to Volterra-Fredholm integral equations, see [9][10][11][12].…”