On a study of the representation of solutions of a psi-Caputo fractional differential equations with a single delay


Aydın M., Mahmudov N. I. , Aktuglu H., Baytunc E., Atamert M. S.

ELECTRONIC RESEARCH ARCHIVE, vol.30, no.3, pp.1016-1034, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.3934/era.2022053
  • Journal Name: ELECTRONIC RESEARCH ARCHIVE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.1016-1034
  • Keywords: Mittag-Leffler type matrix function, fractional linear and nonlinear systems, psi-Caputo derivative representation of solutions, delayed perturbation, TRANSFORMS
  • Istanbul Technical University Affiliated: Yes

Abstract

We give a representation of solutions to linear nonhomogeneous psi-fractional delayed differential equations with noncommutative matrices. We newly define psi-delay perturbation of MittagLeffler type matrix function with two parameters and apply the method of variation of constants to obtain the representation of the solutions. We investigate the existence and uniqueness of solutions for a class of psi-fractional delayed semilinear differential equations by using Banach Fixed Point Theorem. Further, we establish the Ulam-Hyers stability result for the analyzed problem. Finally, we provide some examples to illustrate the applicability of our results.