Nonexistence of Finite-Time Stable Equilibria in a Class of Nonlinear Integral Equations Academic Article

abstract

• This brief report studies conditions to ensure the nonexistence of finite-time stable equilibria in a class of systems that are described by means of nonlinear integral equations, whose kernels are part of some Sonine kernel pairs. It is firstly demonstrated that, under certain criteria, a real-valued function that converges in finite-time to a constant value, different from the initial condition, and remains there afterwards, cannot have a Sonine derivative that also remains at zero after some finite time. Then, the concept of equilibrium is generalized to the case of equivalent equilibrium, and it is demonstrated that a nonlinear integral equation, whose kernel is part of some Sonine kernel pair, cannot possess equivalent finite-time stable equilibria. Finally, illustrative examples are presented.

authors

• Munoz Vazquez, Aldo Jonathan

published proceedings

• FRACTAL AND FRACTIONAL

author list (cited authors)

• Munoz-Vazquez, A. J., Martinez-Fuentes, O., & Fernandez-Anaya, G.

citation count

• 0

complete list of authors

• Munoz-Vazquez, Aldo Jonathan||Martinez-Fuentes, Oscar||Fernandez-Anaya, Guillermo

publication date

• 2023

publisher

• MDPI  Publisher

published in

• n2504-3110ISSN  Journal

keywords

• Finite-time Stability
• Fractional Calculus
• Integral Equations
• Sonine Derivatives

Digital Object Identifier (DOI)

• 10.3390/fractalfract7040320

start page

• 320

end page

• 320

volume

• 7

issue

• 4

URL

• http://dx.doi.org/10.3390/fractalfract7040320