On the Existence and Uniqueness for High Order Fuzzy Fractional Differential Equations with Uncertainty

Abstract

A class fuzzy fractional differential equation (FFDE) involving Riemann-LiouvilleH-differentiability of arbitrary orderq>1is considered. Using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions we establish the uniqueness and existence of the solution after determining the equivalent integral form of the solution.

A Review on Fuzzy Differential Equations

“…a solution that comes from the first form of differentiability, and the other from the second form of differentiability. The existence and uniqueness of the solution for FFDEs using Krasnoselskii-Krein-type condition and Nagumo-type condition have been presented in [119], [120].…”

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

“…Conversely if ( ) is the solution in ( ) of fuzzy integral equation (40), ( ) which is constructed by (26) is the solution of initial value problem (24).…”

“…The existence results of solutions for fuzzy fractional initial value problem under generalized differentiability conditions are obtained by Banach fixed point theorem in [25]. In [26], researchers discussed the uniqueness and existence of the solutions for FFDEs with Riemann-Liouville H-differentiability of arbitrary order by using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions. But, the considerations of researchers in [22][23][24][25][26] were restricted to the case of FFDEs with single derivative term.…”

“…In [26], researchers discussed the uniqueness and existence of the solutions for FFDEs with Riemann-Liouville H-differentiability of arbitrary order by using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions. But, the considerations of researchers in [22][23][24][25][26] were restricted to the case of FFDEs with single derivative term. Ngo et al [27] presented that the existence and uniqueness results of the solution for fuzzy Caputo-Katugampola (CK) fractional differential equations with initial value and in [28] proved that the fractional 2 Advances in Fuzzy Systems fuzzy differential equation is not equal to the fractional fuzzy integral equation in general.…”

On Some Existence and Uniqueness Results for a Class of Equations of Order0<α≤1on Arbitrary Time Scales

“…The quantitative behaviour of solutions to ordinary differential equations on time scales is currently undergoing active investigations. Many authors studied the existence and the uniqueness of the solutions of initial and boundary differential equations; see [8,[10][11][12][13][14][15][16][17][18][19][20] and the references cited therein. In the papers [21][22][23][24][25], several authors were interested by the existence and uniqueness of the first-order differential equations on time scales with initial or boundary conditions using diverse techniques and conditions.…”