Solvability of BVPs for impulsive fractional differential equations involving the Riemann-Liouvile fractional derivatives

Authors

  • Yuji LIU Department of Mathematics and Statistics Guangdong University of Finance and Economics Guangzhou 510320, P.R. China, e-mail: liuyuji888@sohu.com

DOI:

https://doi.org/10.24193/subbmath.2018.1.06

Keywords:

Impulsive fractional differential equation, boundary value problem, Riemann-Liouville fractional derivative.

Abstract

In this paper, we study two classes of BVPs for impulsive fractional differential equations. Some existence results for these boundary value problems are established. Some comments on three published papers are made.

Mathematics Subject Classification (2010): 34K37, 34K45, 34B37, 34B15, 34B10, 92D25, 34A37, 34K15.

References

Agarwal, R., Hristova, S., O’Regan, D., Stability of solutions to impulsive Caputo fractional differential equations, Electron. J. Diff. Equ., 58(2016), 1-22.

Ahmad, B., Nieto, J.J., Existence of solutions for impulsive anti-periodic boundary value problems of fractional order, Taiwan. J. Math., 15(2011), no. 3, 981-993.

Bai, Z., Dong, X., Yin, C., Existence results for impulsive nonlinear fractional differential equation with mixed boundary conditions, Boundary Value Problems, 1(2016), 1-11.

Belmekki, M., Nieto, J.J., Rodriguez-L´opez, R., Existence of solution to a periodic boundary value problem for a nonlinear impulsive fractional differential equation, Electron. J. Qual. Theory Differ. Equ., 16(2014), 27 pages.

Hilfer, R., Application of Fractional Calculus in Physics, World Scientific Publishing Company, Singapore, 2000.

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Frational Differential Equations, Elsevier Science B.V., Amsterdam, 2006.

Kilbas, A.A., Trujillo, J.J., Differential equations of fractional order: methods, results and problems, I, Appl. Anal., 78(2001), 153–192.

Kosmatov, N., Initial value problems of fractional order with fractional impulsive conditions, Results. Math., 63(2013), 1289-1310.

Liu, Y., Studies on impulsive differential models with multi-term Riemann-Liouville fractional derivatives, Journal of Applied Mathematics and Computing, 522016, no. 1-2, 529-565.

Liu, Y., On piecewise continuous solutions of higher order impulsive fractional differential equations and applications, Appl. Math. Comput., 287(2016), 38-49.

Liu, Y., Survey and new results on boundary-value problems of singular fractional differential equations with impulse effects, Electron. J. Differ. Equ, 16(2016), 296.

Mawhin, J., Topological degree methods in nonlinear boundary value problems, in: NS- FCBMS Regional Conference Series in Math., American Math. Soc. Providence, RI, 1979.

Rehman, M., Eloe, P.W., Existence and uniqueness of solutions for impulsive fractional differential equations, Appl. Math. Comput., 224(2013), 422-431.

Wang, H., Lin, X., Anti-periodic BVP of fractional order with fractional impulsive conditions and variable parameter, J. Appl. Math. Comput.

Wang, J., Zhang, Y., On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives, Appl. Math. Letters, 39(2015), 85-90.

Wang, J., Zhou, Y., Feckan, M., On recent developments in the theory of boundary value problems for impulsive fractional differential equations, Comput. Math. Appl., 64(10)(2012), 3008-3020.

Zhao, K., Impulsive fractional differential equation higher order problems of the higher- order fractional differential equation with eigenvalue arguments, Adv. Differ. Equ., 382(2015) 16 pages.

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Published

2018-03-30

How to Cite

LIU, Y. (2018). Solvability of BVPs for impulsive fractional differential equations involving the Riemann-Liouvile fractional derivatives. Studia Universitatis Babeș-Bolyai Mathematica, 63(1), 79–108. https://doi.org/10.24193/subbmath.2018.1.06

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