Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Mathematics
Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad
Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad
Mathematics and System Engineering Faculty Publications
In this paper, we develop the existence theory for nonlinear second-order ordinary differential equations equipped with new kinds of nonlocal non-separated type integral multi-point boundary conditions on an arbitrary domain. Existence results are proved with the aid of fixed point theorems due to Schaefer, Krasnoselskii, and Leray–Schauder, while the uniqueness of solutions for the given problem is established by means of contraction mapping principle. Examples are constructed for the illustration of the obtained results. Ulam-stability is also discussed for the given problem. A variant of the problem involving different boundary data is also discussed. Finally, we introduce an associated boundary …
Lyapunov Functions To Caputo Fractional Neural Networks With Time-Varying Delays, Ravi P. Agarwal, Snezhana G. Hristova, Donal O'Regan
Lyapunov Functions To Caputo Fractional Neural Networks With Time-Varying Delays, Ravi P. Agarwal, Snezhana G. Hristova, Donal O'Regan
Mathematics and System Engineering Faculty Publications
One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when …