ON THE BLOWING UP SOLUTIONS OF A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we are concerned with the study of the system of fractional differential equations ^cD₀₊^α X(t) = Γ(α)(t + 1)^k1 X^a(t)Y ^q(t), 0 < α < 1, t > 0, ^cD₀₊^β Y (t) = Γ(β)(t + 1)^k2 Y ^b(t)X^p(t), 0 < β < 1, t > 0, subject to X(0) = X0 > 0, Y (0) = Y0 > 0, where Γ(σ) stands for the Gamma function, ^cD₀₊^α stands for the Caputo fractional derivative, and a, b, p, q, k1, and k2 are real numbers that will be specified later. We present sufficient conditions for the non-existence of global solutions. Furthermore, we present the asymptotic growth of blowing-up solutions near the blow up time, and the graphical profile of the blowing-up solutions.