Representation of solutions to fuzzy linear fractional differential equations with a piecewise constant argument

Abstract

This study marks the first exploration of fuzzy linear fractional differential equations with a piecewise constant argument (FLFDEs-PCA), incorporating the concept of Caputo's type gH-differentiability with the order $\alpha \in (0,1]$. Such problems are noteworthy as they represent hybrid systems, blending the characteristics of continuous and discrete dynamical systems and integrating aspects from both differential and difference equations. The primary objective of this research is to establish a standardized framework for deriving explicit solution formulas for FLFDEs-PCA under various scenarios. Additionally, illustrative examples are provided to demonstrate the practical implications of our theoretical findings.