Analysis and Optimal Control of φ-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions
Sarra Guechi, Rajesh Dhayal, Amar Debbouche, Muslim Malik
Abstract
The goal of this paper is to consider a new class of φ-Hilfer fractional differential equations with impulses and nonlocal conditions. By using fractional calculus, semigroup theory, and with the help of the fixed point theorem, the existence and uniqueness of mild solutions are obtained for the proposed fractional system. Symmetrically, we discuss the existence of optimal controls for the φ-Hilfer fractional control system. Our main results are well supported by an illustrative example.
Topics & Concepts
SemigroupUniquenessMathematicsFractional calculusFixed-point theoremApplied mathematicsClass (philosophy)Fixed pointOptimal controlDifferential equationMathematical analysisMathematical optimizationComputer scienceArtificial intelligenceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems