Stabilization of coupled systems of quadratic integral equations of Chandrasekhar type

Abstract

We present existence theorems for coupled system of quadratic integral equations of generalized Chandrasekhar type which has numerous application (cf. , , and ). Also, the asymptotic stability of solutions will be considered.

Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type

“…is continuous. Recently, in 2017, Hashem and El-Sayed [19] considered the following two-dimensional quadratic Chandrasekhar integral equations:…”

“…[17] to model the process of radiative transfer. From this date onward, this type has attracted a lot of attention from many researchers [18][19][20][21].…”

Nonlinear quadratic Volterra-Urysohn functional-integral equations in Orlicz spaces

“…Equation ( 2) describes scattering through a homogeneous semi-infinite plane atmosphere and discontinuous solutions for such equation are useful estimation of non-homogeneous atmosphere (cf. [7,19]), then solutions in Orlicz spaces are imperious (see also some comments in [12]). Such equations have applications in various branches such as in traffic theory, kinetic theory of gases, in the theory of radiative transfer, in the theory of neutron transport, and in mathematical physics (cf.…”

“…Most of the papers were devoted to study quadratic integral equations in Banach algebras (cf. [5,19], for example). These equations were also discussed in some Banach-Orlicz algebras (cf.…”

On the solvability of a general class of a coupled system of stochastic functional integral equations

“…At the same time examining coupled systems associated with integral equations is important as well, because such systems model many physical problems, (see e.g. El-Sayed & Al-Fadel, 2018;Hashem & El-Sayed, 2017;Zhang, 2018). Recently ( 1.2) where 0 < b j < 1, j ¼ 1, 2, and J b j is the Riemann-Liouville fractional order integral operator.…”