Theory of hybrid differential equations on time scales

Document Type : Research Paper


1 School of Mathematical Sciences‎, ‎University of Jinan‎, ‎Jinan‎, ‎Shandong 250022‎, ‎P.R‎. ‎China.

2 School of Electrical Engineering‎, ‎University of‎ ‎Jinan‎, ‎Jinan‎, ‎Shandong 250022‎, ‎P.R‎. ‎China.


‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎comparison principle is proved which will be useful for further‎ ‎study of qualitative behavior of solutions‎. ‎Our results in this ‎paper extend and improve some known results.


Main Subjects

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