Existence, Uniqueness, and Eq–Ulam-Type Stability of Fuzzy Fractional Differential Equation
Azmat Ullah Khan Niazi, Jia Wei He, Ramsha Shafqat, Bilal Ahmed
Abstract
This paper concerns with the existence and uniqueness of the Cauchy problem for a system of fuzzy fractional differential equation with Caputo derivative of order q∈(1,2], 0cD0+qu(t)=λu(t)⊕f(t,u(t))⊕B(t)C(t),t∈[0,T] with initial conditions u(0)=u0,u′(0)=u1. Moreover, by using direct analytic methods, the Eq–Ulam-type results are also presented. In addition, several examples are given which show the applicability of fuzzy fractional differential equations.
Topics & Concepts
UniquenessMathematicsType (biology)Fractional calculusOrder (exchange)Differential equationStability (learning theory)Initial value problemPure mathematicsApplied mathematicsMathematical analysisComputer scienceEconomicsEcologyFinanceMachine learningBiologyFuzzy Systems and OptimizationNonlinear Differential Equations AnalysisFractional Differential Equations Solutions