Periodic Solutions of the Discrete Fractional Relaxation Equation - Dhawan, Sangeeta; Jonnalagadda, Jagan Mohan (Discontinuity, Nonlinearity, and Complexity, 2026)
A relaxation equation refers to a mathematical model that describes how a system approaches equilibrium or steady-state over time, often after being disturbed. It essentially involves an exponential decay towards a steady state, with a characteristic time that governs how quickly the system relaxes to equilibrium. Relaxation equations are common in many fields like physics, chemistry, engineering, and economics. Motivated by these facts, in this article, we consider the discrete fractional relaxation equation and establish sufficient conditions on the existence, uniqueness and stability of its periodic solutions using suitable fixed point theorems. We also demonstrate the applicability of established results through an example.