Abstract
In this paper, we deal with maximum principles for multi-term space-time variable-order Riesz-Caputo fractional differential equations (MT-STVO-RCFDEs, for short). We firstly derive several important inequalities for variable-order fractional derivatives at extreme points. Based on these inequalities, we obtain the maximum principles. Finally, these principles are employed to show that the uniqueness of solutions of the (MT-STVO-RCFDEs) and continuous dependance of solutions on initial-boundary value conditions.
Acknowledgements
This research has been supported by NNSF of China Grants Nos. 11271087, 61263006 and NSF of Guangxi Grant No. 2014GXNSFDA118002, Special Funds of Guangxi Distinguished Experts Construction Engineering and Science Research Project 2014 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities. And the authors would like to express their sincere thanks to Prof. Yuri Luchko and Prof. Virginia Kiryakova for their very helpful comments and suggestions, which greatly improved the quality of this paper.
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Please cite to this paper as published in:
Fract. Calc. Appl. Anal., Vol. 19, No 1 (2016), pp. 188–211, DOI: 10.1515/fca-2016-0011
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