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On the asymptotic behavior of solutions of certain integro-differential equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Grace, Said R. Graef, John R. Tunç, Ercan |
| Copyright Year | 2019 |
| Abstract | The authors present conditions under which every positive solution x(t) of the integro–differential equation x′′(t) = a(t) + ∫ t c (t − s)α−1[e(s) + k(t, s)f(s, x(s))]ds, c > 1, α > 0, satisfies x(t) = O(tA(t)) as t → ∞, i.e, lim supt→∞ x(t) tA(t) < ∞,where A(t) = ∫ t c a(s)ds. From the results obtained, they derive a technique that can be applied to some related integro–differential equations that are equivalent to certain fractional differential equations of Caputo type of any order. |
| Starting Page | 1305 |
| Ending Page | 1318 |
| Page Count | 14 |
| File Format | PDF HTM / HTML |
| DOI | 10.11948/2156-907X.20180226 |
| Volume Number | 9 |
| Alternate Webpage(s) | http://jaac.ijournal.cn/ch/reader/create_pdf.aspx?file_no=JAAC-2018-0226&journal_id=jaac |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
