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

Huichol Choi,Sunae Pak,Kinam Sin,Sung-Ryol So

doi:10.1155/2019/6457548

Abstract

In this paper, the fuzzy multiterm fractional differential equation involving Caputo-type fuzzy fractional derivative of order 0<α<1 is considered. The uniqueness of solution is established by using the contraction mapping principle and the existence of solution is obtained by Schauder fixed point theorem.

Highlights

Nowadays the fractional differential equations (FDEs) are powerful tools representing many problems in various areas such as control engineering, diffusion processes, signal processing, and electromagnetism.Recently the fuzzy fractional differential equations (FFDEs) have been studied by many researchers in order to analyze some systems with fuzzy initial conditions
The fuzzy fractional differential equations (FFDEs) have been studied by many researchers in order to analyze some systems with fuzzy initial conditions
It is too difficult to find the exact solutions of most FFDEs representing real-world phenomena

Summary

Introduction

Nowadays the fractional differential equations (FDEs) are powerful tools representing many problems in various areas such as control engineering, diffusion processes, signal processing, and electromagnetism. The fuzzy fractional differential equations (FFDEs) have been studied by many researchers in order to analyze some systems with fuzzy initial conditions. In [22], the existence and uniqueness of the solutions of fuzzy initial value problems of fractional differential equations with the Caputo-type fuzzy fractional derivative have been proved. 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. Based on the above facts, in this paper, we study the existence and uniqueness of solutions for fuzzy multiterm fractional differential equations of order 0 < α < 1 with fuzzy initial value under Caputo-type H-differentiability.

Preliminaries and Basic Results

Existence of Solution for Fuzzy Multiterm Fractional Differential Equation

Continuous Dependence on Initial Condition of Solution

Conclusions