TY - JOUR
T1 - ON THE BLOWING UP SOLUTIONS OF A SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS
AU - Ahmad, Sofwah
AU - Kirane, Mokhtar
N1 - Publisher Copyright:
© 2025 American Institute of Mathematical Sciences. All rights reserved.
PY - 2025/2
Y1 - 2025/2
N2 - 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 Xa(t)Y q(t), 0 < α < 1, t > 0, cD0+β Y (t) = Γ(β)(t + 1)k2 Y b(t)Xp(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.
AB - 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 Xa(t)Y q(t), 0 < α < 1, t > 0, cD0+β Y (t) = Γ(β)(t + 1)k2 Y b(t)Xp(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.
KW - Asymptotic growth of blowing up solutions
KW - Blow-up time
KW - Fractional derivative
KW - Non-existence of global solutions
UR - https://www.scopus.com/pages/publications/85210740735
U2 - 10.3934/dcdss.2024081
DO - 10.3934/dcdss.2024081
M3 - Article
AN - SCOPUS:85210740735
SN - 1937-1632
VL - 18
SP - 405
EP - 425
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
IS - 2
ER -