Monotone iterative method for fractional differential equations
| dc.contributor.author | Bai, Zhanbing | |
| dc.contributor.author | Zhang, Shuo | |
| dc.contributor.author | Sun, Sujing | |
| dc.contributor.author | Yin, Chun | |
| dc.date.accessioned | 2023-05-25T19:02:15Z | |
| dc.date.available | 2023-05-25T19:02:15Z | |
| dc.date.issued | 2016-01-06 | |
| dc.description.abstract | In this article, by using the lower and upper solution method, we prove the existence of iterative solutions for a class of fractional initial value problem with non-monotone term Dα0+ u(t) = ƒ(t, u(t)), t ∈ (0, h), t1-α u(t)|t=0 = u0 ≠ 0, where 0 < h < +∞, ƒ ∈ C([0, h] x ℝ, ℝ), Dα0+ u(t) is the standard Riemann-Liouville fractional derivative, 0 < α < 1. A new condition on the nonlinear term is given to guarantee the equivalence between the solution of the IVP and the fixed-point of the corresponding operator. Moreover, we show the existence of maximal and minimal solutions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 8 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Bai, Z., Zhang, S., Sun, S., & Yin, C. (2016). Monotone iterative method for fractional differential equations. Electronic Journal of Differential Equations, 2016(06), pp. 1-8. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16878 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional initial value problem | |
| dc.subject | Lower and upper solution method | |
| dc.subject | Existence of solutions | |
| dc.title | Monotone iterative method for fractional differential equations | |
| dc.type | Article |