Blowing-up Solutions of Distributed Fractional Differential Systems

Bashir AHMAD; Ahmed ALSAEDI; Mokhtar KIRANE

doi:10.1016/j.chaos.2021.110747

Blowing-up Solutions of Distributed Fractional Differential Systems

Bashir AHMAD
, Ahmed ALSAEDI
, Mokhtar KIRANE

Mathematics

King Abdulaziz University

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

7 Scopus citations

Abstract

We first show that any solution to a nonlinear equation involving a distributed fractional derivative blows-up in a finite time. Then we extend our analysis to a system of nonlinear equations involving distributed fractional derivatives of different orders with different weight functions. Our results rely on the non-linear capacity method.

Original language	British English
Article number	110747
Journal	Chaos, Solitons and Fractals
Volume	145
DOIs	https://doi.org/10.1016/j.chaos.2021.110747
State	Published - Apr 2021

Keywords

blow-up
Distributed fractional derivative
Hölder's inequality
system of equations
ε-Young's inequality

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10.1016/j.chaos.2021.110747

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title = "Blowing-up Solutions of Distributed Fractional Differential Systems",

abstract = "We first show that any solution to a nonlinear equation involving a distributed fractional derivative blows-up in a finite time. Then we extend our analysis to a system of nonlinear equations involving distributed fractional derivatives of different orders with different weight functions. Our results rely on the non-linear capacity method.",

keywords = "blow-up, Distributed fractional derivative, H{\"o}lder's inequality, system of equations, ε-Young's inequality",

author = "Bashir AHMAD and Ahmed ALSAEDI and Mokhtar KIRANE",

note = "Funding Information: This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (RG-42-130-41). The authors, therefore, acknowledge with thanks DSR technical and financial support. We also thank the reviewer for his constructive remarks on our work. Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

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AU - ALSAEDI, Ahmed

AU - KIRANE, Mokhtar

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PY - 2021/4

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N2 - We first show that any solution to a nonlinear equation involving a distributed fractional derivative blows-up in a finite time. Then we extend our analysis to a system of nonlinear equations involving distributed fractional derivatives of different orders with different weight functions. Our results rely on the non-linear capacity method.

AB - We first show that any solution to a nonlinear equation involving a distributed fractional derivative blows-up in a finite time. Then we extend our analysis to a system of nonlinear equations involving distributed fractional derivatives of different orders with different weight functions. Our results rely on the non-linear capacity method.

KW - blow-up

KW - Distributed fractional derivative

KW - Hölder's inequality

KW - system of equations

KW - ε-Young's inequality

UR - https://www.scopus.com/pages/publications/85100643265

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DO - 10.1016/j.chaos.2021.110747

M3 - Article

AN - SCOPUS:85100643265

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VL - 145

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

M1 - 110747

ER -

Blowing-up Solutions of Distributed Fractional Differential Systems

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