The profile of blowing-up solutions to a nonlinear system of fractional differential equations

Abstract

We investigate the profile of the blowing up solutions to the nonlinear nonlocal system (FDS) u (t) + D α 0 + (u − u 0)(t) = |v(t)| q , t > 0, v (t) + D β 0 + (v − v 0)(t) = |u(t)| p , t > 0, where u(0) = u 0 > 0, v(0) = v 0 > 0, p > 1, q > 1 are given constants and D α 0 + and D β 0 + , 0 < α < 1, 0 < β < 1 stand for the Riemann-Liouville fractional derivatives. Our method of proof relies on comparisons of the solution to the (FDS) with solutions of the subsystems obtained from (FDS) by dropping either the usual derivatives or the fractional derivatives.

Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

“…Indeed fractional calculus tools have numerous applications in nanotechnology, control theory, viscoplasticity flow, biology, signal and image processing etc, see the latest monographs, [9], [10], [11], [12], [13] articles [14], [15] and reference therein. The mathematical analysis of initial and boundary value problems (linear or nonlinear) of fractional differential equations has been studied extensively by many authors, we refer to [16], [17] , [18], [19], [20] and references therein.…”

Blowing-up solutions for a nonlinear time-fractional system

“…for u > 0, v > 0 and 0 < α, β < 1. Then Kirane and Malik in [4] studied the profile of the blowing-up solutions of system (1.2). The study of the reduced system:…”

Blowing‐up solutions to two‐times fractional differential equations

“…However, papers on nonlinear fractional differential equations are scarce [9], [10]. Multi-time differential equations appear for example in analyzing oscillators as used very recently by Narayan and Roychowdhury [12].…”