Approximate Controllability of Ψ-Hilfer Fractional Neutral Differential Equation with Infinite Delay
C. S. Varun Bose, R. Udhayakumar, Subramanian Velmurugan, M. Saradha, Barakah Almarri
Abstract
In this paper, we explain the approximate controllability of Ψ-Hilfer fractional neutral differential equations with infinite delay. The outcome is demonstrated using the infinitesimal operator, fractional calculus, semigroup theory, and the Krasnoselskii’s fixed point theorem. To begin, we emphasise the presence of the mild solution and show that the Ψ-Hilfer fractional system is approximately controllable. Additionally, we present theoretical and practical examples.
Topics & Concepts
ControllabilitySemigroupMathematicsFixed-point theoremFractional calculusInfinitesimalFixed pointOperator (biology)Differential equationApplied mathematicsMathematical analysisGeneTranscription factorRepressorBiochemistryChemistryNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsNumerical methods for differential equations