Langevin Equations with Generalized Proportional Hadamard–Caputo Fractional Derivative
Mohamed A. Barakat, Ahmed H. Soliman, Abd‐Allah Hyder
Abstract
We look at fractional Langevin equations (FLEs) with generalized proportional Hadamard-Caputo derivative of different orders. Moreover, nonlocal integrals and nonperiodic boundary conditions are considered in this paper. For the proposed equations, the Hyres-Ulam (HU) stability, existence, and uniqueness (EU) of the solution are defined and investigated. In implementing our results, we rely on two important theories that are Krasnoselskii fixed point theorem and Banach contraction principle. Also, an application example is given to bolster the accuracy of the acquired results.
Topics & Concepts
Hadamard transformUniquenessMathematicsLangevin equationFixed-point theoremFractional calculusApplied mathematicsMathematical analysisContraction principleBanach fixed-point theoremStability (learning theory)Derivative (finance)Banach spacePhysicsStatistical physicsComputer scienceFinancial economicsEconomicsMachine learningFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations