Finite time blow-up of solutions for a nonlinear system of fractional differential equations
| dc.contributor.author | Mennouni, Abdelaziz | |
| dc.contributor.author | Youkana, Abderrahmane | |
| dc.date.accessioned | 2022-06-06T13:33:16Z | |
| dc.date.available | 2022-06-06T13:33:16Z | |
| dc.date.issued | 2017-06-25 | |
| dc.description.abstract | In this article we study the blow-up in finite time of solutions for the Cauchy problem of fractional ordinary equations ut + α1 cDα0+ u + α2 cDα20+ u + ⋯ + αn cDαn0+ = ∫t0 (t - s)γ1 / Γ(1 - γ1) ƒ(u(s), v(s))ds, vt + b1 cDβ10+ v + b2 cDβ20+ v + ⋯ + bn cDβn0+ v = ∫t0 (t - s)-γ2 / Γ(1 - γ2) g(u(s), v(s))ds, for t > 0, where the derivatives are Caputo fractional derivatives of order αi, βi, and ƒ and g are two continuously differentiable functions with polynomial growth. First, we prove the existence and uniqueness of local solutions for the above system supplemented with initial conditions, then we establish that they blow-up in finite time. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Mennouni, A., & Youkana, A. (2017). Finite time blow-up of solutions for a nonlinear system of fractional differential equations. Electronic Journal of Differential Equations, 2017(152), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15845 | |
| 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, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional differential equation | |
| dc.subject | Caputo fractional derivative | |
| dc.subject | Blow-up in finite time | |
| dc.title | Finite time blow-up of solutions for a nonlinear system of fractional differential equations | |
| dc.type | Article |