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Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations.
- Source :
-
Journal of Mathematical Physics . May2024, Vol. 65 Issue 5, p1-23. 23p. - Publication Year :
- 2024
-
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]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIFFERENTIAL equations
*DEFINITE integrals
*DELAY differential equations
Subjects
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 65
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 177609109
- Full Text :
- https://doi.org/10.1063/5.0159480