Comparative analysis on the blow-up occurrence of solutions to Hadamard type fractional differential systems

Abstract

The main intention of this paper is to deal with the weak singularity of solutions to some nonlinear Hadamard type fractional differential systems (HTFDSs) which could be viewed as the generalization of classic Hadamard fractional settings. Resorting to the lower and upper solutions technique and constructing the compatible weighted Banach space, the completely continuous operator described by Hadamard type fractional versions as well as a sufficient criterion for the existence of blow-up solutions to some nonlinear HTFDSs is established. Additionally, the comparative analysis on the blow-up rate affected by critical system parameters is also presented, and several examples clearly illustrate the effectiveness and efficiency of the proposed results.

Keywords:

• Hadamard type fractional calculus
• generalized Lipschitz condition
• completely continuous operator
• lower and upper solutions technique
• blow-up phenomena

2010 Mathematics Subject Classifications:

• 26A33
• 74H35

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant No. 11902108), the Natural Science Foundation of Anhui Province (Grant No. 1908085QA12), and the Fundamental Research Funds for the Central Universities of China (Grant No. JZ2021HGTB0125). The author is grateful to the anonymous referees for careful reading of this manuscript and valuable comments. And the author would like to thank the help from the editors too.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was financially supported by the National Natural Science Foundation of China (Grant No. 11902108), the Natural Science Foundation of Anhui Province (Grant No. 1908085QA12), and the Fundamental Research Funds for the Central Universities of China (Grant No. JZ2021HGTB0125).