Contents I. Introduction
Fractional calculus and its potential applications have gained a lot of importance because fractional calculus has become a powerful tool with more accurate and successful results in modeling several complex phenomena in numerous seemingly diverse and widespread fields of science and engineering. Many fields such as aerodynamics and control systems, signal processing, bioengineering and biomedical. In recent years, fractional differential equation and dynamical systems have been proved to be valuable tools in the modeling of many phenomena in various fields of engineering, physics, economics. It draws a great application in fields such as viscoelasticity, heat conduction in materials with memory and in fluid dynamic traffic model, see the basic books and the interesting paper [4, 5 , 7 , 11] . In [8, 10] , the author introduced a new concept of fractional integral and derivative based on the Riemann-Liouville and the Hadamard integral and derivative into a single form. For further results based on the new fractional derivative, in [9] author investigated the existence and uniqueness results of solution for fractional differential equations of Caputo-Katugampola derivative type by using the Schauder's second fixed point theorem. In [2], authors studied the existence and uniqueness theorem of an initial value problem for Caputo-Katugampola fractional differential equations and a numerical method is also proposed to solve this problem. In [1], a general form of fractional Gronwall inequality type with dependence on the Caputo-Katugampola fractional derivative is presented to estimate the difference between two solutions of two initial value problems. In [6], the existence and uniqueness of an initial value problem of Riemann-Liouville-Katugampola fractional differential equations is studied. In [12], authors proposed a discrete version of the Caputo-Katugampola derivative and obtained numerical formulae to solve a linear fractional differential equation with Caputo-Katugampola fractional derivative. In [3], the chaotic behavior and stability results of fractional differential equations within Caputo-Katugampola derivative are investigated. Since one of interesting subjects in this area, in this paper, we consider the fuzzy generalized fractional differential equations of Caputo-Katugampola type as follows: \begin{equation*}c_{D_{a}^{\alpha p}\psi(t)}=f(t,\psi(t)^{C}D_{a}^{(\alpha-1)p}\psi(t)), \psi(a)=\psi_{0}, \psi^{\prime}(a)=\xi_{0}, \tag{1.1}\end{equation*}
