A Brief Review on Fuzzy Fractional Differential Equations and Their Applications

Differential equation is a very important topic of interest for continuous system modelling as well as theoretical purposes. For real-life situation modelling, several variations are used by scientists and engineers. A fractional differential equation is one of them. Due to several reasons, such as measurement difficulty and environmental noise, the data set for real-life modelling is sometimes imprecise in nature. Fuzzy set theory is one of the suitable ideologies to deal with uncertainty. When a fuzzy set is associated with a fractional differential equation, then fuzzy fractional differential equations (FFDEs) come. Fuzzy fractional differential equations have garnered significant attention due to their ability to model processes with uncertainty and memory dependence in various scientific and theoretical contexts. Also, the concepts are applied to various engineering sciences and technical applications for modelling real-life problems. This review paper provides a comprehensive summary of FFDEs, a key concept in theoretical advancements, solution methodologies, and practical applications. The study examines previously published materials and conducts a comparative analysis of several components. The different crisp and fuzzy fractional derivatives are also compared with respect to different components. The various forms of past FFDEs are described, along with their theoretical and practical applications. Finally, tasks and probable future research directions in this emerging field are outlined.