EXISTENCE RESULTS FOR ABC-FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED AND INTEGRAL TYPE OF BOUNDARY CONDITIONS
Nayyar Mehmood, AHSAN ABBAS, Thabet Abdeljawad, Ali Akgül
Abstract
This paper presents a study on the existence theory of fractional differential equations involving Atangana–Baleanu (AB) derivative of order [Formula: see text], with non-separated and integral type boundary conditions. An existence result for the solutions of given AB-fractional differential equation is proved using Krasnoselskii’s fixed point theorem, while the uniqueness of the solution is obtained using Banach contraction principle. Some conditions are proposed under which the given boundary value problem is Hyers–Ulam stable. Examples are given to validate our results.
Topics & Concepts
MathematicsContraction principleUniquenessFixed-point theoremMathematical analysisFractional calculusBoundary value problemType (biology)Picard–Lindelöf theoremContraction mappingIntegral equationBiologyEcologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems