EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS
Amita Devi, Anoop Kumar, Thabet Abdeljawad, Aziz Khan
Abstract
In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.
Topics & Concepts
MathematicsUniquenessFixed-point theoremMathematical analysisContraction principleType (biology)Nonlinear systemFixed pointContraction mappingBanach fixed-point theoremStability (learning theory)Fractional calculusBoundary value problemContraction (grammar)Applied mathematicsPhysicsMachine learningComputer scienceMedicineQuantum mechanicsInternal medicineBiologyEcologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisStability and Controllability of Differential Equations