Abstract
The Gronwall inequality, which plays a very important role in clasical differential equations, is generalized to the fractional differential equations with Hadamard derivatives in this paper. According to the inequality, we investigate the dependence of the solution on both the order and the initial conditions to the fractional differential equations with Hadamard derivatives. Furthermore, in terms of the inequality, the estimation of the bound of the Lyapunov exponents for the Hadamard type fractional differential systems is considered.
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Acknowledgements
This work was partially supported by the National Natural Science Foundation of China under Grant no. 10872119 and Shanghai Leading Academic Discipline Project under Grant no. S30104.
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Gong, Z., Qian, D., Li, C., Guo, P. (2012). On the Hadamard Type Fractional Differential System. In: Baleanu, D., Machado, J., Luo, A. (eds) Fractional Dynamics and Control. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0457-6_13
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DOI: https://doi.org/10.1007/978-1-4614-0457-6_13
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