Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses-Reference-Cited by-同舟云学术

Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses

Published:2019-04-01 Issue:2 Volume:22 Page:495-508
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Borah Jayanta¹,Nandan Bora Swaroop¹

Affiliation:

1. Department of Mathematics , Indian Institute of Technology Guwahati , Guwahati , 781039 , India

Abstract

Abstract In this article, we establish a set of sufficient conditions for the existence of mild solution of a class of fractional differential equations with not instantaneous impulses. The results are obtained by using Banach fixed point theorem and Krasnoselskii’s fixed point theorem. An example is presented for validation of result.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2019-0029/pdf

Reference29 articles.

1. S. Abbas, M. Benchohra, M.A. Darwish, New stability results for partial fractional differential inclusions with not instanttaneous impulses. Fract. Calc. Appl. Anal. 18, No 1 (2015), 172–191; 10.1515/fca-2015-0012; https://www.degruyter.com/view/j/fca.2015.18.issue-1/issue-files/fca.2015.18.issue-1.xml.

2. R. Agarwal, S. Hristova, D. O’Regan, A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations. Fract. Calc. Appl. Anal. 19, No 2 (2016), 290–318; 10.1515/fca-2016-0017; https://www.degruyter.com/view/j/fca.2016.19.issue-2/issue-files/fca.2016.19.issue-2.xml.

3. R. Agarwal, S. Hristova, D. O’Regan, Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions. J. Franklin Inst. 354 (2017), 3097–3119.

4. R. Agarwal, D. O’Regan, Stability of Caputo fractional differential equations with non-instantaneous impulses. Commun. Appl. Anal. 20, No 1 (2016), 149–174.

5. R. Agarwal, S. Hristova, D. O’Regan, Non-instantaneous impulses in Caputo fractional differential eqquations. Fract. Calc. Appl. Anal. 20, No 3 (2017), 595–622; 10.1515/fca-2017-0032; https://www.degruyter.com/view/j/fca.2017.20.issue-3/issue-files/fca.2017.20.issue-3.xml.

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