On the existence and uniqueness of solutions for fuzzy fractional differential equations

Abstract

In this paper, we introduce and define a new metric on the space of fuzzy continuous functions in the fractional calculus. Regarding this metric and using the well-known Banach fixed point theorem, we provide some conditions that guarantee the existence and uniqueness of solution to a nonlinear fuzzy fractional differential equation in the proposed metric. Finally, two examples are given to illustrate the results.

Controllability of Fuzzy Solutions for Neutral Impulsive Functional Differential Equations with Nonlocal Conditions

“…The existence and uniqueness for fuzzy impulsive functional differential equations have been studied by Vu H, Van Hao N (2016) under generalized Hukuhara differentiability, using contraction mapping [4]. Rivaz et al (2017) introduced and defined a new metric on the space of fuzzy continuous functions in the fractional calculus. They established particular conditions that assured the existence and uniqueness of a solution to a nonlinear fuzzy fractional differential equation using the Banach fixed point theorem [17].…”

“…Rivaz et al (2017) introduced and defined a new metric on the space of fuzzy continuous functions in the fractional calculus. They established particular conditions that assured the existence and uniqueness of a solution to a nonlinear fuzzy fractional differential equation using the Banach fixed point theorem [17]. Some basic results on fuzzy differential equations can be found in [18][19][20][21].…”

Existence and Continuous Dependence on Initial Data of Solution for Initial Value Problem of Fuzzy Multiterm Fractional Differential Equation

“…Therefore, research about FFDEs can be classified into two classes, namely, existence of solution and numerical methods. Many theoretical researches have been advanced on the existence, uniqueness, and stability of solution of FFDEs [1][2][3][4][5][6][7][8][9][10][11][12].…”