Global Asymptotic Stability for a Stationary Solution of a System of Integro-Differential Equations Describing the Formation of Liver Zones

Construction of a measure of noncompactness in Sobolev spaces with an application to functional integral-differential equations

“…It arises especially in a variety of models from applied mathematics, biological science, physics and another phenomenon, such as the theory of electrodynamics, electromagnetic, fluid dynamics, heat and oscillating magnetic, etc. [9,12,18,21,24]. There have appeared recently a number of interesting papers [2,6,10,19,22,23,27] on the solvability of various integral equations with help of measures of noncompactness.…”

Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

“…IDEs can be encountered in various fields of science such as physics, chemistry, biology, and engineering. These kinds of equations can also be found in numerous applications, such as electromagnetic, plasma physics, elasticity, fluid dynamics, oscillation theory, polymer rheology, chemical kinetics, biomechanics, and control theory [1][2][3][4][5]. In recent years, nonlinear periodic boundary value problems (BVPs) have been widely studied by many authors [6][7][8][9], due to a wide range of applications in applied mathematics, physics, and engineering, particularly in the homogenization of composite materials with a periodic microstructure [10,11].…”

Utilizing feed-back neural network approach for solving linear Fredholm integral equations system

“…Also Variational iteration method [10], homotopy analysis method [11][12][13][14][15][16][17], Legendre polynomial method [18,19] and Adomian decomposition method [20] are efficacious techniques. Additionally, some other numerical methods applied to solve the integral equations in [21][22][23][24][25][26]. In the most of the introduced approaches the integral equation is transformed to a linear system.…”