Existence and uh-stability of integral boundary problem for a class of nonlinear higher-order Hadamard fractional Langevin equation via Mittag-Leffler functions
Kaihong Zhao
Abstract
The Langevin equation is a very important mathematical model in describing the random motion of particles. The fractional Langevin equation is a powerful tool in complex viscoelasticity. Therefore, this paper focuses on a class of nonlinear higher-order Hadamard fractional Langevin equation with integral boundary value conditions. Firstly, we employ successive approximation and Mittag-Leffler function to transform the differential equation into an equivalent integral equation. Then the existence and uniqueness of the solution are obtained by using the fixed point theory. Meanwhile, the Ulam-Hyers (UH) stability is proved by inequality technique and direct analysis.
Topics & Concepts
MathematicsHadamard transformLangevin equationMathematical analysisUniquenessFractional calculusIntegral equationBoundary value problemNonlinear systemStability (learning theory)Applied mathematicsStatistical physicsPhysicsComputer scienceQuantum mechanicsMachine learningFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations