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

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

Abstract 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–Liouvill...

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Main Authors: Kui Liu, JinRong Wang, Donal O’Regan
Format: Article
Language:English
Published: SpringerOpen 2019-02-01
Series:Advances in Difference Equations
Subjects:
ψ-Hilfer fractional-order delay differential equations
Solutions
Existence
Stability
Online Access:http://link.springer.com/article/10.1186/s13662-019-1997-4
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spelling doaj-412e4a11b69b487c85db7fdd2fa3fd682020-11-25T00:34:37ZengSpringerOpenAdvances in Difference Equations1687-18472019-02-012019111210.1186/s13662-019-1997-4Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equationsKui Liu0JinRong Wang1Donal O’Regan2College of Science, Guizhou Institute of TechnologyDepartment of Mathematics, Guizhou UniversitySchool of Mathematics, Statistics and Applied Mathematics, National University of IrelandAbstract 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.http://link.springer.com/article/10.1186/s13662-019-1997-4ψ-Hilfer fractional-order delay differential equationsSolutionsExistenceStability
collection DOAJ
language English
format Article
sources DOAJ
author Kui Liu
JinRong Wang
Donal O’Regan
spellingShingle Kui Liu
JinRong Wang
Donal O’Regan
Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
Advances in Difference Equations
ψ-Hilfer fractional-order delay differential equations
Solutions
Existence
Stability
author_facet Kui Liu
JinRong Wang
Donal O’Regan
author_sort Kui Liu
title Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
title_short Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
title_full Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
title_fullStr Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
title_full_unstemmed Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
title_sort ulam–hyers–mittag-leffler stability for ψ-hilfer fractional-order delay differential equations
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2019-02-01
description Abstract 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.
topic ψ-Hilfer fractional-order delay differential equations
Solutions
Existence
Stability
url http://link.springer.com/article/10.1186/s13662-019-1997-4
work_keys_str_mv AT kuiliu ulamhyersmittaglefflerstabilityforpshilferfractionalorderdelaydifferentialequations
AT jinrongwang ulamhyersmittaglefflerstabilityforpshilferfractionalorderdelaydifferentialequations
AT donaloregan ulamhyersmittaglefflerstabilityforpshilferfractionalorderdelaydifferentialequations
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