A discussion on approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions
C. Dineshkumar, Kottakkaran Sooppy Nisar, R. Udhayakumar, V. Vijayakumar
Abstract
Abstract In this paper, the approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions in Hilbert spaces is considered. By using the stochastic analysis theory, fractional calculus, multivalued maps, and Karlin's fixed point technique, a new set of necessary and sufficient conditions, are formulated which guarantees the approximate controllability of the nonlinear Hilfer fractional stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, two examples are presented to illustrate the theory of the obtained results.
Topics & Concepts
ControllabilityMathematicsSobolev spaceType (biology)Nonlinear systemHilbert spaceApplied mathematicsFixed-point theoremFractional calculusDifferential inclusionDifferential (mechanical device)Fixed pointMathematical analysisEngineeringAerospace engineeringPhysicsBiologyEcologyQuantum mechanicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStability and Controllability of Differential Equations