A coupled system of nonlinear Caputo–Hadamard Langevin equations associated with nonperiodic boundary conditions
Mohammed M. Matar, Jehad Alzabut, Jagan Mohan Jonnalagadda
Abstract
In this paper, we study the coupled system of nonlinear Langevin equations involving Caputo–Hadamard fractional derivative and subject to nonperiodic boundary conditions. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the features of the Hadamard fractional derivative, the implementation of fixed point theorems, and the employment of Urs's stability approach. An example is introduced to facilitate the understanding of the theoretical findings.
Topics & Concepts
Hadamard transformMathematicsUniquenessNonlinear systemStability (learning theory)Boundary value problemFractional calculusMathematical analysisApplied mathematicsFixed-point theoremLangevin equationDerivative (finance)Boundary (topology)Statistical physicsPhysicsComputer scienceFinancial economicsMachine learningEconomicsQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations