On existence and stability results for nonlinear fractional delay differential equations

On existence and stability results for nonlinear fractional delay differential equations

We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hye...

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Bibliographic Details
Main Authors: Kishor D. Kucche, Sagar T. Sutar
Format: Article
Language:English
Published: Sociedade Brasileira de Matemática 2018-10-01
Series:Boletim da Sociedade Paranaense de Matemática
Subjects:
Fractional delay differential equation
Fixed point theorem
Existence and uniqueness
Successive approximation
Ulam > Hyers stability
$ \mathbb{E}_{\alpha}$ > Ulam > Hyers stability.
Online Access:https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/33603
Description
Summary:We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hyers--Rassias stability, $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability and generalized $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability of fractional order delay differential equations.
ISSN:0037-8712
2175-1188

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