Study for System of Nonlinear Differential Equations with Riemann-Liouville Fractional Derivative

Abstract

In this work, we study existence theorem of the initial value problem for the system of fractional differential equations where Dα denotes standard Riemann-Liouville fractional derivative, 0 < α < 1, and A  is a square matrix. At the same time, power-type estimate for them has been given.

Share and Cite:

Y. Zheng and W. Wang, "Study for System of Nonlinear Differential Equations with Riemann-Liouville Fractional Derivative," Applied Mathematics, Vol. 4 No. 7A, 2013, pp. 5-8. doi: 10.4236/am.2013.47A002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] K. M. Furati and N.-E. Tatar, “Power-Type Estmates for a Nonlear Fractional Differential Equation,” Journal of Nonlinear Analysis, Vol. 62, No. 6, 2005, pp. 1025-1036. doi:10.1016/j.na.2005.04.010
[2] V. Daftardar-Gejji and A. Babakhani, “Analysis of a SysTem of Fractional Differential Equations,” Journal of Mathematical Analysis and Applications, Vol. 293, No. 2, 2004, pp. 511-512. doi:10.1016/j.jmaa.2004.01.013
[3] D. Delbosco and L. Rodino, “Existence and Uniqueness for a Nonlinear Fractional Differential Equation,” Journal of Mathematical Analysis and Applications, Vol. 204, No. 2, 1996, pp. 511-512. doi:10.1006/jmaa.1996.0456
[4] I. Podlubny, “Fractional Differential Equtions,” Academic Press, New York, 1999.
[5] R. A. Horn and C. R. Johnson, “Matrix Analysis,” Cambridge University press, London, 1985.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.