Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations

Ahmad M. Ahmad; Khaled M. Furati; Nasser Eddine Tatar

doi:10.1007/s00009-018-1235-4

Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations

Ahmad M. Ahmad^*
, Khaled M. Furati
, Nasser Eddine Tatar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.

Original language	English
Article number	188
Journal	Mediterranean Journal of Mathematics
Volume	15
Issue number	5
DOIs	https://doi.org/10.1007/s00009-018-1235-4
State	Published - 1 Oct 2018

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

Keywords

Asymptotic behavior
Caputo fractional derivative
fractional integro-differential equation
integral inequalities
nonlocal source

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-018-1235-4

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title = "Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations",

abstract = "In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.",

keywords = "Asymptotic behavior, Caputo fractional derivative, fractional integro-differential equation, integral inequalities, nonlocal source",

author = "Ahmad, \{Ahmad M.\} and Furati, \{Khaled M.\} and Tatar, \{Nasser Eddine\}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",

year = "2018",

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doi = "10.1007/s00009-018-1235-4",

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AU - Ahmad, Ahmad M.

AU - Furati, Khaled M.

AU - Tatar, Nasser Eddine

PY - 2018/10/1

Y1 - 2018/10/1

N2 - In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.

AB - In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.

KW - Asymptotic behavior

KW - Caputo fractional derivative

KW - fractional integro-differential equation

KW - integral inequalities

KW - nonlocal source

UR - https://www.scopus.com/pages/publications/85051503169

U2 - 10.1007/s00009-018-1235-4

DO - 10.1007/s00009-018-1235-4

M3 - Article

AN - SCOPUS:85051503169

SN - 1660-5446

VL - 15

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 5

M1 - 188

ER -

Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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