| Title | ON THE SOLUTION OF A NONLINEAR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION |
| Publication Type | Journal Article |
| Year of Publication | 2009 |
| Authors | LIAO, CHUNPING, YE, HAIPING |
| Secondary Title | Communications in Applied Analysis |
| Volume | 13 |
| Issue | 1 |
| Start Page | 57 |
| Pagination | 70 |
| Date Published | 01/2009 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 99Z00. |
| Abstract | This paper investigates the existence of a positive solution to a general scalar delayed population model of fractional order that is a nonlinear fractional functional differential equation by applying a nonlinear alternative of Leray-Schauder type in a cone and the generalization of Gronwall’s lemma for singular kernels, improving previously known results. Further, we show the continuous dependence of the solution on the order and the initial condition of nonlinear fractional functional differential equations and obtain an Mittag-Leffler functional estimate of the solution by virtue of the generalized Gronwall inequality.
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| URL | http://www.acadsol.eu/en/articles/13/1/7.pdf |
| Short Title | NONLINEAR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
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