Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative
Khalid Hilal, Ahmed Kajounı, Hamid Lmou
Abstract
In this work, we discuss the existence and uniqueness of solution for a boundary value problem for the Langevin equation and inclusion with the Hilfer fractional derivative. First of all, we give some definitions, theorems, and lemmas that are necessary for the understanding of the manuscript. Second of all, we give our first existence result, based on Krasnoselskii’s fixed point, and to deal with the uniqueness result, we use Banach’s contraction principle. Third of all, in the inclusion case, to obtain the existence result, we use the Leray–Schauder alternative. Last but not least, we give an illustrative example.
Topics & Concepts
UniquenessMathematicsContraction principleBoundary value problemMathematical analysisFixed-point theoremBoundary valuesLangevin equationFractional calculusDerivative (finance)Contraction (grammar)Applied mathematicsStatistical physicsEconomicsMedicineFinancial economicsInternal medicinePhysicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems