On the nonexistence of global solutions for a class of fractional integro-differential problems

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

doi:10.1186/s13662-017-1105-6

On the nonexistence of global solutions for a class of fractional integro-differential problems

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

^*Corresponding author for this work

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

7 Scopus citations

Abstract

We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of the involved parameters, ensuring the nonexistence of global solutions are determined. Unlike the existing results, the source term considered is, in general, a convolution and therefore nonlocal in time. The class of problems we consider includes problems with sources that are polynomials and fractional integrals of polynomials in the state as special cases. Singular kernels illustrating interesting cases in applications are provided and discussed. Our results are obtained by considering a weak formulation of the problem with an appropriate test function and several appropriate estimations.

Original language	English
Article number	59
Journal	Advances in Difference Equations
Volume	2017
Issue number	1
DOIs	https://doi.org/10.1186/s13662-017-1105-6
State	Published - 1 Dec 2017

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).

Keywords

Riemann-Liouville fractional derivative
fractional integro-differential equation
global solution
nonexistence
nonlocal source

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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Cite this

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abstract = "We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of the involved parameters, ensuring the nonexistence of global solutions are determined. Unlike the existing results, the source term considered is, in general, a convolution and therefore nonlocal in time. The class of problems we consider includes problems with sources that are polynomials and fractional integrals of polynomials in the state as special cases. Singular kernels illustrating interesting cases in applications are provided and discussed. Our results are obtained by considering a weak formulation of the problem with an appropriate test function and several appropriate estimations.",

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AU - Ahmad, Ahmad M.

AU - Furati, Khaled M.

AU - Tatar, Nasser Eddine

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Y1 - 2017/12/1

N2 - We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of the involved parameters, ensuring the nonexistence of global solutions are determined. Unlike the existing results, the source term considered is, in general, a convolution and therefore nonlocal in time. The class of problems we consider includes problems with sources that are polynomials and fractional integrals of polynomials in the state as special cases. Singular kernels illustrating interesting cases in applications are provided and discussed. Our results are obtained by considering a weak formulation of the problem with an appropriate test function and several appropriate estimations.

AB - We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of the involved parameters, ensuring the nonexistence of global solutions are determined. Unlike the existing results, the source term considered is, in general, a convolution and therefore nonlocal in time. The class of problems we consider includes problems with sources that are polynomials and fractional integrals of polynomials in the state as special cases. Singular kernels illustrating interesting cases in applications are provided and discussed. Our results are obtained by considering a weak formulation of the problem with an appropriate test function and several appropriate estimations.

KW - Riemann-Liouville fractional derivative

KW - fractional integro-differential equation

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KW - nonexistence

KW - nonlocal source

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SN - 1687-1839

VL - 2017

JO - Advances in Difference Equations

JF - Advances in Difference Equations

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On the nonexistence of global solutions for a class of fractional integro-differential problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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