dc.contributor.author |
Abdeljawad, Thabet
|
|
dc.contributor.author |
Alzabut, Jehad
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|
dc.contributor.author |
Jarad, Fahd
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|
dc.date.accessioned |
2018-09-11T13:19:15Z |
|
dc.date.available |
2018-09-11T13:19:15Z |
|
dc.date.issued |
2017-10-11 |
|
dc.identifier.citation |
Abdeljawad, T., Alzabut, J., Jarad, F. (2017). A generalized Lyapunov-type inequality in the frame of conformable derivatives. Advance in Difference Equations, 321. http://dx.doi.org/10.1186/s13662-017-1383-z |
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dc.identifier.issn |
1687-1847 |
|
dc.identifier.uri |
http://hdl.handle.net/20.500.12416/1690 |
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dc.description.abstract |
We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed. |
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dc.language.iso |
eng |
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dc.publisher |
Springer |
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dc.relation.isversionof |
10.1186/s13662-017-1383-z |
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dc.rights |
info:eu-repo/semantics/openAccess |
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dc.subject |
Lyapunov Inequality |
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dc.subject |
Conformable Derivative |
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dc.subject |
Green's Function |
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dc.subject |
Boundary Value Problem |
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dc.subject |
Sturm-Liouville Eigenvalue Problem |
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dc.title |
A generalized Lyapunov-type inequality in the frame of conformable derivatives |
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dc.type |
article |
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dc.relation.journal |
Advance in Difference Equations |
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dc.contributor.authorID |
234808 |
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dc.identifier.volume |
321 |
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dc.contributor.department |
Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü |
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