Approximate controllability results for Sobolev‐type delay differential system of fractional order without uniqueness
V. Vijayakumar, R. Udhayakumar, Yong Zhou, N. Sakthivel
Abstract
Abstract The main aim of this article is to focus on approximate controllability for Sobolev‐type fractional control problems in Hilbert spaces without uniqueness. By using the fixed point theorem for multivalued maps with nonconvex values, the main results of our article are proved. Moreover, we obtain some results on the continuity of the solution map and the topological structure of the solution set of the considered Sobolev‐type fractional differential system. Finally, we provide a theoretical application to assist in the effectiveness of our discussion.
Topics & Concepts
ControllabilityMathematicsSobolev spaceUniquenessType (biology)Fixed-point theoremOrder (exchange)Mathematical analysisHilbert spaceApplied mathematicsPure mathematicsSet (abstract data type)Computer scienceBiologyFinanceEcologyProgramming languageEconomicsNonlinear Differential Equations AnalysisStability and Controllability of Differential EquationsFractional Differential Equations Solutions