Existence, uniqueness and Ulam's stabilities for a class of implicit impulsive Langevin equation with Hilfer fractional derivatives
Xiaoming Wang, Rizwan Rizwan, Jung Rey Lee, Akbar Zada, Syed Omar Shah
Abstract
<abstract> In this manuscript, a class of implicit impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness, Ulam-Hyers, generalized Ulam-Hyers, Ulam-Hyers-Rassias and generalized Ulam-Hyers-Rassias stability results of our proposed model, with the help of Banach's fixed point theorem. An example is provided at the end to illustrate our results. </abstract>
Topics & Concepts
UniquenessMathematicsClass (philosophy)Fixed-point theoremApplied mathematicsNonlinear systemBanach spaceFixed pointStability (learning theory)Pure mathematicsLangevin equationMathematical analysisStatistical physicsComputer sciencePhysicsMachine learningArtificial intelligenceQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results