Existence and stability results for nonlocal boundary value problems of fractional order
Vedat Suat Ertürk, Amjad Ali, Kamal Shah, Pushpendra Kumar, Thabet Abdeljawad
Abstract
Abstract In this paper, we prove the existence and uniqueness of solutions for the nonlocal boundary value problem (BVP) using Caputo fractional derivative (CFD). We derive Green’s function and give some estimation for it to derive our main results. The main principles applied to investigate our results are based on the Banach contraction fixed point theorem and Schauder fixed point approach. We dwell in detail on some results concerning the Hyers-Ulam (H-U) type and generalized H-U (g-H-U) type stability also for problem we are considering. We justify our results with an illustrative example.
Topics & Concepts
MathematicsUniquenessFixed-point theoremBoundary value problemContraction mappingContraction principleFractional calculusSchauder fixed point theoremType (biology)Order (exchange)Mathematical analysisFixed pointStability (learning theory)Banach fixed-point theoremApplied mathematicsFunction (biology)Picard–Lindelöf theoremComputer scienceEvolutionary biologyBiologyEconomicsEcologyMachine learningFinanceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFunctional Equations Stability Results