Fuzzy Approximate Solutions of Matrix-Valued Fractional Differential Equations by Fuzzy Control Functions
Safoura Rezaei Aderyani, Reza Saadati, Donal O’Regan, Fehaid Salem Alshammari
Abstract
We apply Mittag–Leffler-type functions to introduce a class of matrix-valued fuzzy controllers which help us to propose the notion of multi-stability (MS) and to obtain fuzzy approximate solutions of matrix-valued fractional differential equations in fuzzy spaces. The concept of multi stability allows us to obtain different approximations depending on the different special functions that are initially chosen. Additionally, using various properties of a function of Mittag–Leffler type, we study the Ulam–Hyers stability (UHS) of the models.
Topics & Concepts
MathematicsFuzzy logicStability (learning theory)Matrix (chemical analysis)Applied mathematicsMatrix functionDifferential equationType (biology)Mathematical analysisSymmetric matrixComputer scienceArtificial intelligenceQuantum mechanicsEigenvalues and eigenvectorsPhysicsBiologyMaterials scienceMachine learningComposite materialEcologyFunctional Equations Stability ResultsFractional Differential Equations SolutionsFuzzy Systems and Optimization