( ω , c ) $(\omega ,c)$ -Periodic solutions for time varying impulsive differential equations

Abstract

In this paper, we study a class of (ω, c)-periodic time varying impulsive differential equations and establish the existence and uniqueness results for (ω, c)-periodic solutions of homogeneous problem as well as nonhomogeneous problem.

Reconfigurable Liquid‐Bodied Miniature Machines: Magnetic Control and Microrobotic Applications

“…[115] One of the critical factors in controlling liquid metal-based machines is the driving force of the miniature soft devices. Various driven mechanisms have been proposed, including selfpropulsion (e.g., bubble propulsion, [116][117][118][119] self-electrophoretic propulsion, [120][121][122][123][124][125] enzyme-powered robots [126,127] ), Marangoni effect-based locomotion, [128][129][130] and external fields-driven navigation (e.g., magnetic field, [131][132][133][134] electric field, [135][136][137][138][139][140][141][142] ultrasound, [143,144] light [145][146][147] ). Magnetically driven liquid metal-based robots are usually driven by permanent magnets or electromagnets.…”

A system for fluid pumping by liquid metal multi-droplets

“…The electrocapillary effect refers to the change in interfacial tension at the liquid-liquid interface caused by an electric field. 20 The motion and deformation of room-temperature liquid metals are typical examples of applications of the electrocapillary effect, [21][22][23][24][25][26][27][28] playing a crucial role in the control of a small amount of liquid. Yun et al 29 reported a small-scale pump designed based on the electrocapillary effect, which utilized the reciprocating motion of a mercury droplet under an electric field to alternately open the inlet and outlet chambers, achieving the directed transport of a small amount of liquid.…”

(ω,c)-Periodic Solution to Semilinear Integro-Differential Equations with Hadamard Derivatives

“…Ren and Wang [9] established a required and sufficient criterion for (ω, c)-periodic solutions to impulsive fractional differential equations and investigated the existence and uniqueness of solutions via Caputo derivatives to impulsive fractional differential equations in Banach spaces. For further information on the existence and uniqueness of solutions to impulsive and regular fractional differential equations, see [10][11][12][13][14]. We also examined fractional oscillators, fractional dynamical systems, and the periodic solution of fractional oscillation equations in [15][16][17].…”