OSCILLATION ANALYSIS IN FRACTIONAL VECTOR PDES: A DETAILED QUANTITATIVE AND QUALITATIVE APPROACH

Fractional differential equations have gained significant attention for modeling complex processes across various fields such as porous structures, electrical networks, and industrial robotics. They offer a versatile framework for understanding phenomena with self-similar properties, viscoelasticity, and more. This paper delves into the study of oscillatory solutions, a crucial aspect of fractional differential equations, shedding light on their quantitative and qualitative characteristics.While oscillatory behavior in scalar fractional ordinary differential equations has received some attention in previous research, this paper extends the analysis to scalar fractional partial differential equations, a less-explored area. By exploring oscillations in this broader context, we contribute to a deeper understanding of complex processes modeled by fractional differential equations.