On the linear fuzzy model associated with Caputo–Fabrizio operator

Abstract

In this paper, we introduce the fuzzy Caputo-Fabrizio operator under generalized Hukuhara differentiability concept. In this setting, we study the linear fuzzy fractional initial value problems and present the general form of their solutions. Some examples are given to illustrate our results.

A Review on Fuzzy Differential Equations

“…FFDEs under the concept of Caputo-Fabrizio fractional derivative in combination with SGH-derivative (Caputo-Fabrizio SGH-derivative) were studied in 2018 [142]. The main reason why such a derivative was introduced is that the kernel in Caputo-Fabrizio fractional derivative, unlike Riemann-Liouville and Caputo's derivatives, is non-singular.…”

Study on Fuzzy Fractional European Option Pricing Model with Mittag-Leffler Kernel

“…Many fuzzy fractional differential operators are known to be nonlocal, indicating that their future states depend on their historical and current states. A range of singular and non-singular fuzzy fractional operators have been developed with applications in a wide range of fields of science, including fuzzy Riemann-Liouville derivative [4], fuzzy generalized Hukuhara Caputo fractional derivative [13,29], fuzzy Caputo-Fabrizio fractional derivative [1,21], fuzzy Atangana-Baleanu fractional derivative [7], fuzzy Riemann-Liouville-Katugampola generalized Hukuhara fractional derivative [18], fuzzy Caputo-Katugampola generalized Hukuhara fractional derivative [18], fuzzy conformable fractional derivative [15,16].…”

“…In order to obtain the fuzzy solution of the fuzzy model (1), we first define the fuzzy Atangana-Baleanu fractional derivative based on generalized Hukuhara differentiability (𝐴𝐵𝐶 𝑔𝐻 − derivative), followed by proof of the fact that the model has a solution based on the type of 𝐴𝐵𝐶 𝑔𝐻 −differentiability, and this is the only solution. Finally, we use the the fuzzy homotopy perturbation transform method (FHPTM) to solve the fuzzy Black Scholes problem.…”

Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative

“…Boundary value problems with CF derivatives have been studied in [9,10]. In [11] a linear fuzzy model with CF operator is studied, and the (i, α) and (ii, α) differentiable solutions of the model are obtained. In [12], some good examples presented, which justify that CF derivatives are much more needed to describe real problems.…”