Four-point Nonlocal Boundary Conditions Research Articles

Analysis of multipoint impulsive problem of fractional-order differential equations

This manuscript is related to establishing appropriate results for the existence and uniqueness of solutions to a class of nonlinear impulsive implicit fractional-order differential equations (FODEs). It is remarkable that impulsive differential equations have attracted great popularity due to various important applications in the mathematical modeling of real-world phenomena/processes, particularly in biological or biomedical engineering domains as well as in control theory. The mentioned problem is considered under four-point nonlocal boundary conditions and the derivative is taken in the Caputo sense. Our results are based on fixed-point theorems due to Banach and Schaefer. To justify our results, two suitable examples are given.

The properties of Green’s functions for one stationary problem with nonlocal boundary conditions

In this paper we research Green’s function properties for stationary problem with four-pointnonlocal boundary conditions. Dependence of these functions on values ξ and γ is investigated. Green’sfunctions graphs with various values ξ and γ are presented.