Mathematics (Jun 2021)

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

  • Gani Stamov,
  • Ivanka Stamova

DOI
https://doi.org/10.3390/math9121413
Journal volume & issue
Vol. 9, no. 12
p. 1413

Abstract

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In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.

Keywords