Finite time blow-up of solutions for a nonlinear system of fractional differential equations
Date
2017-06-25
Authors
Mennouni, Abdelaziz
Youkana, Abderrahmane
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Fractional differential equation, Caputo fractional derivative, Blow-up in finite time
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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.