Abstract
In this paper, we study boundary value problems for fractional differential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence of solutions are established by virtue of fractional calculus and fixed point method under some mild conditions. Two examples are given to illustrate the results.
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This work is supported by Tianyuan Special Funds of the National Natural Science Foundation of China (Grant No. 11026102), National Natural Science Foundation of China (Grant Nos. 10971173, 10961009), National Natural Science Foundation of Guizhou Province (2010, No. 2142).
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Wang, J., Lv, L. & Zhou, Y. Boundary value problems for fractional differential equations involving Caputo derivative in Banach spaces. J. Appl. Math. Comput. 38, 209–224 (2012). https://doi.org/10.1007/s12190-011-0474-3
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DOI: https://doi.org/10.1007/s12190-011-0474-3
Keywords
- Boundary value problems
- Fractional differential equations
- Generalized singular Gronwall inequality
- Existence of solutions