Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness
Jizhao Huang, Danfeng Luo
Abstract
In this article, we consider conformable fractional stochastic differential equations (CFSDEs) driven by fBm with infinite delay via measures of noncompactness (MNC). As far as we know, there are few papers considering this issue. First, by virtue of a Mönch fixed point theorem and MNC, we explore the existence of solutions for CFSDEs. Subsequently, with the aid of Jensen inequality, Hölder inequality, stochastic analysis techniques, and semigroup theory, the controllability for this considered CFSDEs is investigated by employing a Mönch fixed point theorem. Thereafter, the controllability of CFSDEs with nonlocal conditions is discussed. Finally, the theoretical result is supported through an example.
Topics & Concepts
ControllabilityMathematicsFixed-point theoremSemigroupApplied mathematicsConformable matrixMathematical analysisFractional calculusFixed pointPure mathematicsQuantum mechanicsPhysicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStability and Controllability of Differential Equations