Symmetry (Nov 2021)

Analysis and Optimal Control of <i>φ</i>-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions

  • Sarra Guechi,
  • Rajesh Dhayal,
  • Amar Debbouche,
  • Muslim Malik

DOI
https://doi.org/10.3390/sym13112084
Journal volume & issue
Vol. 13, no. 11
p. 2084

Abstract

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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.

Keywords