Fuzzy Conformable Fractional Differential Equations

Abstract

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>q</a:mi> <a:mo>∈</a:mo> <a:mfenced open="(" close="]" separators="|"> <a:mrow> <a:mn>0,1</a:mn> </a:mrow> </a:mfenced> </a:math> .