Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses-Reference-Cited by-同舟云学术

Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses

Published:2017-07-14 Issue:4 Volume:67 Page:875-894
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Abbas Saïd¹,Benchohra Mouffak²³

Affiliation:

1. Laboratory of Mathematics University of Saïda PO Box 138, 20000 Saïda Algeria

2. Laboratory of Mathematics University of Sidi Bel-Abbes P.O. Box 89 , Sidi Bel-Abbès Algeria

3. Department of Mathematics Faculty of Science, King Abdulaziz University P.O. Box 80203 , Jeddah Saudi Arabia

Abstract

Abstract In this paper, we shall present some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces. Some examples are also provided to illustrate our results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0017/pdf

Reference31 articles.

1. Abbas, S.—Benchohra, M.: Darboux problem for partial functional differential equations with infinite delay and Caputo’s fractional derivative, Adv. Dyn. Syst. Appl. 5 (2010), 1–19.

2. Abbas, S.—Benchohra, M.: Impulsive partial hyperbolic functional differential equations of fractional order with state-dependent delay, J. Fract. Calc. Appl. 13 (2010), 225–244.

3. Abbas, S.—Benchohra, M.—Diagana, T.: Existence and attractivity results for some fractional order partial integro-differential equations with delay, Afr. Diaspora J. Math. 15 (2013), 87–100.

4. Abbas, S.—Benchohra, M.—Gorniewicz, L.: Fractional order impulsive partial hyperbolic functional differential equations with variable times and state-dependent delay, Math. Bulletin 7 (2010), 317–350.

5. Abbas, S.—Benchohra, M.— N’guérékata, G. M.: Topics in Fractional Differential Equations, Springer, New York, 2012.

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