Synchronization of the Circadian Rhythms with Memory: A Simple Fractional-Order Dynamical Model Based on Tow Coupled Oscillators

Disruptions of the circadian rhythm are associated with internal desynchronization. It affects some functions our body and behavior that important to health. Our modern lifestyle has contributed millions people developing disruptions, making subject very clinically as well economically. Motivated by studying a simple mathematical model can reveal features synchronization desynchronization, in this contribution, we extend coupling oscillator phase proposed Strogatz [14] sense memory is considered modeling. Such result introduction Caputo-type fractional derivatives oscillators’ dynamics, resulting model. We show well-posed. Furthermore, analyzethe phenomena. obtain synchronized solutions explicitly when equally distributed between oscillators. In contrast, distinct levels imposed modeling, lower upper bounds because any existing solution must be confined between. present numerical realizations support theoretical findings great detail.