Non-instantaneous impulses in Caputo fractional differential equations

Ravi Agarwal; Snezhana Hristova; Donald O'Regan

doi:10.13025/26209

Non-instantaneous impulses in Caputo fractional differential equations

Ravi Agarwal
, Snezhana Hristova
, Donald O'Regan

Mathematics

Texas A&M University-Kingsville
University of Plovdiv Paisii Hilendarski

Research output: Contribution to a Journal (Peer & Non Peer) › Review article › peer-review

72 Citations (Scopus)

Abstract

Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.

Original language	English
Pages (from-to)	595-622
Number of pages	28
Journal	Fractional Calculus and Applied Analysis
Volume	20
Issue number	3
DOIs	https://doi.org/10.13025/26209 https://doi.org/10.1515/fca-2017-0032
Publication status	Published - 27 Jun 2017

Keywords

boundary-value problem
Caputo fractional differential equation
existence
lyapunov functions
non-instantaneous impulses
stability

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10.13025/26209Licence: CC BY
10.1515/fca-2017-0032

Cite this

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abstract = "Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.",

keywords = "boundary-value problem, Caputo fractional differential equation, existence, lyapunov functions, non-instantaneous impulses, stability",

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AU - Hristova, Snezhana

AU - O'Regan, Donald

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Y1 - 2017/6/27

N2 - Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.

AB - Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.

KW - boundary-value problem

KW - Caputo fractional differential equation

KW - existence

KW - lyapunov functions

KW - non-instantaneous impulses

KW - stability

UR - http://hdl.handle.net/10379/10134

UR - https://www.scopus.com/pages/publications/85021769360

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DO - 10.13025/26209

M3 - Review article

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JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 3

ER -

Non-instantaneous impulses in Caputo fractional differential equations

Abstract

Keywords

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