Solution estimates to Caputo proportional fractional derivative delay integro-differential equations


Tunç O., Tunç C.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.117, no.1, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 117 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s13398-022-01345-y
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: CPFrDIDE, Generalized Caputo proportional fractional derivative, Multiple delays, Stability, Boundedness, LYAPUNOV FUNCTIONS, STABILITY ANALYSIS, BOUNDEDNESS, INTEGRABILITY
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this article, a class of scalar generalized Caputo proportional fractional derivative delay integro-differential equations (CPFrDIDEs) with multiple non-linear kernels and multiple time delays is considered. Fundamental qualitative behaviors of the solutions such as stability, asymptotic stability, exponential stability, and boundedness of solutions are investigated. The technique used in the proofs depend upon the modified Lyapunov-Razumikhin method (LRM). As numerical applications of the novel results of this article, four examples are constructed to demonstrate that the results are valid and applicable. The outcomes of this article allow novel contributions to qualitative theory of FrDIDEs.