Basics of Fractional and Fuzzy Fractional Differential Equations - Tapaswini, Smita; Chakraverty, Snehashish; Behera, Diptiranjan (Fuzzy Arbitrary Order System, 2016)
This chapter presents some preliminaries related to fuzzy differential equations and fractional and fuzzy fractional differential equations. It considers the nth‐order fuzzy initial value problem (FIVP), where a fuzzy function is the Hukahara fuzzy derivatives, continuous on some interval, subject to fuzzy initial conditions. The chapter also presents the fractional derivative in the Caputo sense. It derives the n‐th order fuzzy boundary value problem (FBVP), where a fuzzy function is continuous on some interval, subject to fuzzy boundary conditions, and determines its solution. The chapter combines differential equations of fractional order and with uncertainty and considers a new type of dynamical system, that is, fuzzy differential equations of fractional order. It defines the following fractional initial value problem (FrIVP) subject to the initial conditions. The chapter finally discusses the fuzzy fractional initial value problem (FFIVP) subject to the fuzzy initial conditions.