Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

Asadzade J. A., Mahmudov N. I.

JOURNAL OF MATHEMATICAL PHYSICS, vol.65, no.5, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.1063/5.0159480
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, MathSciNet, zbMATH, DIALNET
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this write-up, we focus on pseudo-Hilfer-type fractional order delayed differential equations with bounded definite integral initial conditions on the time interval [0, T]. We begin by establishing relevant lemmas. Then, we derive the solution to the homogeneous Hilfer-type pseudo-fractional order retarded differential equation that satisfies the appropriate initial condition using classical methods. Next, we obtain explicit formulas for solutions to linear inhomogeneous Hilfer-type pseudo-fractional time retarded differential equations with constant coefficients, employing classical ideas. Furthermore, we investigate the existence and uniqueness of the solution of the Hilfer-type pseudo-fractional order delayed differential equation and demonstrate the stability of the given differential equation in the Ulam-Hyers sense on the time interval [0, T].