Existence of solution for a coupled system of Urysohn-Stieltjes functional integral equations

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

“…Our results offer a generalization to the results developed by A.M.A. El-Sayed et al in (El-Sayed & Kenawy, 2014a, 2014b. In the future, many models can be investigated, such as fractal integral systems (Volterra or Fredholm) with more concentration on the singular types (He, 2020).…”

“…The uniqueness of the solution is investigated for Equations (1.1), and (1.2) as well. But due to some unexpected disturbance which may effect the accuracy of the system, we believe that stochastic models give more accurate results than the proposed models in (El-Sayed & Kenawy, 2014a, 2014b, see for more details (Elborai, Abdou, & Youssef, 2013a, 2013bElborai & Youssef, 2019;Klyatskin, 2015;Umamaheswari, Balachandran, & Annapoorani, 2017, 2018. Therefore, our aim in this article is to generalize the deterministic models 1.1, and 1.2 to the stochastic form in a suitable sense.…”

Weak Solutions of a Coupled System of Urysohn‐Stieltjes Functional (Delayed) Integral Equations

“…where g I × I → R is nondecreasing in the second argument (see [1]) and the symbol d s indicates the integration with respect to s. Equations of type (1) and some of their generalizations were considered in the paper (see [2]). We remark here that when E = R, these types of equations have been studied by Banaś (see [1][2][3][4][5]) and also by some other authors, for example (see [6][7][8][9][10] and for coupled systems [11]). For the solutions in a reflexive Banach space (see [12,13]).…”

Existence of solutions of a coupled system of functional integro-differential equations of arbitrary (fractional) orders

“…During the past few years, some investigators have established a lot of useful and interesting coupled system of functional equations, in order to achieve various goals; see [1][2][3][4][5][6], and the references cited therein. In this paper, we are concerned with the coupled system of functional integro-differential equations    dx dt = f 1 (t, D α y(t), D β x(t)), t ∈ (0, T ], The existence of at least one solution (x, y), x, y ∈ C 1 [0, T ] is proved, under certain conditions.…”