
AIMS Mathematics, 2020, 5(4): 33313345. doi: 10.3934/math.2020214.
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Nonlocal problems of fractional systems involving left and right fractional derivatives at resonance
1 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2 College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
Received: , Accepted: , Published:
Keywords: fractional system; left and right fractional derivative; nonlocal problem; resonance condition
Citation: Xiping Liu, Mei Jia, Zhanbing Bai. Nonlocal problems of fractional systems involving left and right fractional derivatives at resonance. AIMS Mathematics, 2020, 5(4): 33313345. doi: 10.3934/math.2020214
References:
 1. A. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science Limited, 2006.
 2. I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering, Academic Press, 1999.
 3. K. Diethelm, The analysis of fractional differential equations, SpringerVerlag, Berlin, 2010.
 4. K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, JohnWily and Sons, New York, 1993.
 5. Y. Zhou, Basic Theory of fractional differential equations, World Scientific, Singapore, 2014.
 6. Q. Song, Z. Bai, Positive solutions of fractional differential equations involving the RiemannStieltjes integral boundary condition, Adv. Differ. Equ., 2018 (2018), 183.
 7. X. Zhao, Y. Liu, H. Pang, Iterative positive solutions to a coupled fractional differential system with the multistrip and multipoint mixed boundary conditions, Adv. Differ. Equ., 2019 (2019), 123.
 8. Y. Tian, S. Sun, Z. Bai, Positive solutions of fractional differential equations with pLaplacian, J. Funct. Space., 2017 (2017).
 9. G. C. Wu, D. Baleanu, Z. Deng, et al. Lattice fractional diffusion equation in terms of a RieszCaputo difference, Physica A: Statistical Mechanics and its Applications, 438 (2015), 335339.
 10. X. Liu, M. Jia, W. Ge, The method of lower and upper solutions for mixed fractional fourpoint boundary value problem with pLaplacian operator, Appl. Math. Lett., 65 (2017), 5662.
 11. S. K. Ntouyas, J. Tariboon, P. Thiramanus, Mixed problems of fractional coupled systems of RiemannLiouville differential equations and Hadamard integral conditions, J. Comput. Anal. Appl., 21 (2016), 813828.
 12. X. Liu, M. Jia, The method of lower and upper solutions for the general boundary value problems of fractional differential equations with pLaplacian, Adv. Differ. Equ., 2018 (2018), 115.
 13. F. Ge, C. Kou, Stability analysis by Krasnoselskii's fixed point theorem for nonlinear fractional differential equations, Appl. Math. Comput., 257 (2015), 308316.
 14. L. Yang, Application of AveryPeterson fixed point theorem to nonlinear boundary value problem of fractional differential equation with the Caputo's derivative, Commun. Nonlinear Sci., 17 (2012), 45764584.
 15. Y. Xu, Z. He, Synchronization of variableorder fractional financial system via active control method, Open Phys., 11 (2013), 824835.
 16. A. Bashir, S. K. Ntouyas, Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions, Appl. Math. Comput., 266 (2015), 615622.
 17. B. Zhu, L. Liu, Y. Wu, Existence and uniqueness of global mild solutions for a class of nonlinear fractional reactiondiffusion equations with delay, Comput. Math. Appl., 78 (2019), 18111818.
 18. M. Fečkan, J. Wang, Periodic impulsive fractional differential equations, Adv. Nonliear Anal., 8 (2019): 482496.
 19. R. Arévalo, A. Garcimartín, D. Maza, Anomalous diffusion in silo drainage, The European Physical Journal E, 23 (2007), 191198.
 20. J. S. Leszczynski, T. Blaszczyk, Modeling the transition between stable and unstable operation while emptying a silo, Granul. Matter, 13 (2011), 429438.
 21. E. Szymanek, The application of fractional order differential calculus for the description of temperature profiles in a granular layer, Advances in the Theory and Applications of Noninteger Order Systems, 257 (2013), 243248.
 22. Y. Tian, J. J. Nieto, The applications of criticalpoint theory to discontinuous fractionalorder differential equations, P. Edinburgh Math. Soc., 60 (2017 ), 10211051.
 23. M. Jia, X. Liu, Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions, Appl. Math. Comput., 232 (2014), 313323.
 24. M. Jia, L. Li, X. Liu, et al. A class of nonlocal problems of fractional differential equations with composition of derivative and parameters, Adv. Differ. Equ., 2019 (2019).
 25. C. Bai, Infinitely many solutions for a perturbed nonlinear fractional boundaryvalue problem, Electron. J. Differ. Equ., 2013 (2013), 112.
 26. M. Galewski, G. M. Bisci, Existence results for onedimensional fractional equations, Math. Method. Appl. Sci., 39 (2016), 14801492.
 27. Y. Zhao, H. Chen, B. Qin, Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods, Appl. Math. Comput., 257 (2015), 417427.
 28. X. Liu, M. Jia, Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives, Appl. Math. Comput., 353 (2019), 230242.
 29. C. Torres, Existence of a solution for the fractional forced pendulum, J. Appl. Math. Comput. Mech., 13 (2014), 125142.
 30. T. Blaszczyk, E. Kotela, M. R. Hall, et al. Analysis and applications of composed forms of Caputo fractional derivatives, Acta Mechanica et Automatica, 5 (2011), 1114.
 31. F. Jiao, Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl. 62 (2011), 11811199.
 32. R. E. Gaines, J. Mawhin, Coincidence degree and nonlinear differential equations, 1977.
Reader Comments
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *