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. <i>Electronic Journal of Differential Equations, 2017</i>(152), pp. 1-15.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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