Analytical analysis of fractional-order sequential hybrid system with numerical application
Aziz Khan, Zareen A. Khan, Thabet Abdeljawad, Hasib Khan
Abstract
Abstract We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. We consider the existence and uniqueness of solutions and the Hyers–Ulam (H-U) stability for a general class. We use the Banach and Leray–Schauder alternative theorems for the existence criteria. With the help of nonnegative Green’s functions, the fractional-order class is turned into m -equivalent integral forms. As an application of our problem, a fractional-order smoking model in terms of the Atangana–Baleanu derivative is presented as a particular case.
Topics & Concepts
UniquenessMathematicsFractional calculusClass (philosophy)Order (exchange)Stability (learning theory)Applied mathematicsFixed-point theoremMathematical analysisPure mathematicsComputer scienceMachine learningEconomicsArtificial intelligenceFinanceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems