Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative
Asma Asma, Sana Shabbir, Kamal Shah, Thabet Abdeljawad
Abstract
Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana-Baleanu-Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain.
Topics & Concepts
MathematicsUniquenessContraction principleOrdinary differential equationFixed-point theoremStability (learning theory)Class (philosophy)Fractional calculusApplied mathematicsMathematical analysisType (biology)Boundary value problemBanach spaceFixed pointDifferential equationEcologyArtificial intelligenceComputer scienceMachine learningBiologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems