Abstract
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.
Highlights
Fractional-order differential systems are generalizations of ordinary-order differential systems and have been widely studied in recent years due to their large potential for applications in numerous domains of science, engineering and practice [1,2,3,4], including some very recent results [5]
Numerous fundamental and qualitative results related to applications of the fractional calculus approach to differential inclusions are available in the existing literature
The important concept of almost periodic waves is introduced to the class of impulsive fractional-order inclusions; The effects of considering impulsive perturbations and fractional-order derivatives on the almost periodic properties are investigated and criteria for existence and uniqueness are established; The main results are obtained by applying the theory of operators semigroup, Hausdorff measure of noncompactness, fixed point theorems and techniques based on fractional calculus; The efficiency of the obtained results is demonstrated on a fractional impulsive
Summary
Fractional-order differential systems are generalizations of ordinary-order differential systems and have been widely studied in recent years due to their large potential for applications in numerous domains of science, engineering and practice [1,2,3,4], including some very recent results [5]. Since the investigations into the existence of non-periodic solutions and their properties are of great significance for fractional-order inclusions, the theory of almost periodic waves should be further developed. The important concept of almost periodic waves is introduced to the class of impulsive fractional-order inclusions; The effects of considering impulsive perturbations and fractional-order derivatives on the almost periodic properties are investigated and criteria for existence and uniqueness are established; The main results are obtained by applying the theory of operators semigroup, Hausdorff measure of noncompactness, fixed point theorems and techniques based on fractional calculus; The efficiency of the obtained results is demonstrated on a fractional impulsive.
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