Biography
Prof. Li MA
Prof. Li MA
School of Mathematics, Hefei University of Technology, China
Title: Studies on the blow-up solutions of Hadamard fractional differential systems
Abstract: 
Compared to classical calculus, due to the non-locality and weak singularity of fractional order operators, there do exist many difficulties and challenges in mathematical analysis and mechanical modeling described by fractional differential equations. Although fractional calculus has developed over three hundred years and has owned many definitions without equivalence to each other. Among them, Hadamard-type fractional calculus has obtained an important position in applied sciences such as rheology, ultra-slow dynamics and material mechanics. In this talk, by constructing proper Banach space and employing lower and upper solutions technique, we prove the existence of the blow-up solutions for a class of Hadamard fractional differential systems (HFDSs). In addition, we establish a more general condition than classical Lipschitz condition which is employed to guarantee the equivalence between the solutions to the HFDS and the corresponding functional operator. Also several examples are presented to verify our theoretical results. 
Keywords:Hadamard-type fractional calculus;existence of blow-up solutions;lower and upper solutions technique