Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations

• Published in: Advances in difference equations Vol. 2019; no. 1; pp. 1 - 12
• Main Authors: Liu, Kui, Wang, JinRong, O’Regan, Donal
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 06-02-2019; Springer Nature B.V; SpringerOpen
• Subjects: Advances in Fractional Differential Equations and Their Real World Applications - Part Two; Analysis; Delay; Difference and Functional Equations; Differential equations; Existence; Functional Analysis; Mathematical analysis; Mathematics; Mathematics and Statistics; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations; Solutions; Stability; ψ-Hilfer fractional-order delay differential equations; Stability; Hilfer fractional-order delay differential equations; Solutions; Existence
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-019-1997-4

In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of
ψ
-Hilfer fractional-order delay differential equations. We use the Picard operator method and a generalized Gronwall inequality involved in a
ψ
-Riemann–Liouville fractional integral. Finally, we give two examples to illustrate our main theorems.