NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS
In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method....
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| Published in | Acta mathematica scientia Vol. 37; no. 1; pp. 119 - 130 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
2017
Department of Mathematics and Statistics,King Fahd University of Petroleum and Minerals,Dhahran,31261,Saudi Arabia |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(16)30120-5 |
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| Abstract | In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part. |
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| AbstractList | In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part. |
| Author | Mohnmmed D, KASSIM Khaled M. FURATI Nasser-eddine TATAR |
| AuthorAffiliation | Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia |
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| Cites_doi | 10.1115/1.3167616 10.2514/3.8142 10.4171/ZAA/1281 10.1016/j.camwa.2009.06.031 10.1122/1.549724 10.1155/2012/391062 10.1155/2013/605029 10.1016/j.camwa.2012.01.009 10.1007/s11202-007-0050-0 10.1016/S0022-247X(02)00394-3 10.1016/j.amc.2006.11.105 10.1016/j.camwa.2010.09.057 10.1515/gmj-2012-0006 10.1016/j.chaos.2006.08.001 10.1016/j.jmaa.2005.03.054 10.1023/A:1016556604320 10.1155/2009/981728 10.1007/s10440-008-9356-6 |
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| Keywords | fractional differential equation nonexistence global solution 26A33 Riemann-Liouville fractional integral and fractional derivative |
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| Notes | nonexistence; global solution; fractional differential equation; Riemann-Liouvillefractional integral and fractional derivative In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part. 42-1227/O |
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| Publisher | Elsevier Ltd Department of Mathematics and Statistics,King Fahd University of Petroleum and Minerals,Dhahran,31261,Saudi Arabia |
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| Snippet | In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the... In this paper,we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the... |
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| SubjectTerms | 26A33 fractional differential equation global solution nonexistence Riemann-Liouville fractional integral and fractional derivative 函数法 分数导数 分数阶 多项式 微分不等式 微分问题 解的存在性 阻尼波动方程 |
| Title | NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS |
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