Existence, stability and controllability results of fractional dynamic system on time scales with application to population dynamics
Vipin Kumar, Muslim Malik
2020International Journal of Nonlinear Sciences and Numerical Simulation15 citationsDOIOpen Access PDF
Abstract
Abstract In this manuscript, we investigate the existence, uniqueness, Hyer-Ulam stability and controllability analysis for a fractional dynamic system on time scales. Mainly, this manuscript has three segments: In the first segment, we give the existence of solutions. The second segment is devoted to the study of stability analysis while in the last segment, we establish the controllability results. We use the Banach and nonlinear alternative Lery-Schauder–type fixed point theorem to establish these results. Also, we give some numerical examples for different time scales. Moreover, we give two applications to outline the effectiveness of these obtained results.
Topics & Concepts
ControllabilityUniquenessStability (learning theory)MathematicsNonlinear systemFixed-point theoremApplied mathematicsBanach fixed-point theoremPopulationControl theory (sociology)Mathematical analysisComputer scienceControl (management)PhysicsSociologyArtificial intelligenceQuantum mechanicsDemographyMachine learningNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFunctional Equations Stability Results