Abstract
This paper is concentrated on the following coupled system of the nonlinear fractional differential equation
where \( f,\;K,\;g,\;H:\;\left[ {0,\,1} \right]\, \times \,\Re \, \to \,\left[ {0,\, + \infty } \right) \) are the positive continuous functions. \( D^{\alpha } \) and \( D^{\beta } \) are the standard Riemann–Liouville fractional derivatives with the order \( \alpha ,\, \beta, \) respectively. We give the existence and the uniqueness of the solution by using the Schauder fixed point theorem and the generalized Gronwall inequality.
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Acknowledgments
This work was supported by the Tian Yuan Specialized Research Fund for Mathematics (No. 11226167), the Natural Science Foundation of Hainan Province (No. 111005), the Scientific Research Foundation of Hainan Province Education Bureau (No. Hjkj2011-19), and the Ph.D. Scientific Research Starting Foundation of Hainan Normal University (No. HSBS1016).
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Li, Yl., Lin, Sy. (2013). Boundary Value Problem for a Coupled System of Nonlinear Fractional Differential Equation. In: Yin, Z., Pan, L., Fang, X. (eds) Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013. Advances in Intelligent Systems and Computing, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37502-6_17
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DOI: https://doi.org/10.1007/978-3-642-37502-6_17
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