Citation: Djamila Chergui, Taki Eddine Oussaeif, Merad Ahcene. Existence and uniqueness of solutions for nonlinear fractional differential equations depending on lower-order derivative with non-separated type integral boundary conditions[J]. AIMS Mathematics, 2019, 4(1): 112-133. doi: 10.3934/Math.2019.1.112
| [1] | A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, In: North-Holland Mathematics Studies, Amsterdam: Elsevier Science, 2006. |
| [2] | A. Granas, J. Dugundji, Fixed Point Theory, New York: Springer, 2003. |
| [3] | B. Ahmad, J. J. Nieto, Existence of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations, Abstr. Appl. Anal., 2009 (2009), ID: 494720. |
| [4] | B. Ahmad, A. Alsaedi, B. Alghamdi, Analytic approximation of soltions of the forced Duffing equation with integral boundary conditions, Nonlinear Anal: Real World Appl., 9 (2008), 1727—1740. |
| [5] | B. Ahmad, J. J. Nieto, A. Alsaedi, Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions, Acta Math. Sci., 31 (2011), 2122—2130. |
| [6] | B. Ahmad, S. K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions, Fract. Calc. Appl. Anal., 15 (2012), 362—382. |
| [7] | D. Baleanu, J. A. T. Machado, A. C. J. Luo, Fractional Dynamics and Control, New York: Springer, 2012. |
| [8] | F. Yan, M. Zuo, X. Hao, Positive solution for a fractional singular boundary value problem with p-Laplacian operator, Bound. Value Probl., 2018 (2018), 1—10. |
| [9] | I. Podlubny, Fractional Differenrial Equations, San Diego: Academic Press, 1999. |
| [10] | J. Sabatier, O. P. Agrawal, J. A. T. Machado, Advances in Fractional Calculus - Theoretical Developments and Applications in Physics and Engineering, Dordrecht: Springer, 2007. |
| [11] | R. P. Agarwal, M. Meehan, D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press & Beijing World Publishing Corporation, 2008. |
| [12] | S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, USA: Gordon and Breach Science Publishers, 1993. |
| [13] | S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differ. Eq., 2006 (2006), 1—12. |
| [14] | V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, 2009. |
| [15] | X. Hao, H.Wang, Positive solutions of semipositone singular fractional differenrial systems with a parameter and integral boundary conditions, Open Math., 16 (2018), 581—596. |
| [16] | X. Hao, H. Sun, L. Liu, Existence results for fractional integral boundary value problem involving fractional derivatives on an infinite interval, Math. Meth. Appl. Sci., 41 (2018), 6984—6996. |
| [17] | X. Liu, Z. Liu, Separated boundary value problem for fractional differential equations depending on lower-order derivative, Adv. Differ. Equations, 2013 (2013), 1—11. |
| [18] | X. Y. Liu, Y. L. Liu, Fractional differential equations with fractional non-separated boundary conditions, Electron. J. Differ. Eq., 2013 (2013), 1—13. |
| [19] | Y. F. Sun, Z. Zeng, J. Song, Existence and uniqueness for the boundary value Problems of nonlinear fractional differential equations, Appl. Math., 8 (2017), 312—323. |
Djamila Chergui, Taki Eddine Oussaeif, Merad Ahcene. Existence and uniqueness of solutions for nonlinear fractional differential equations depending on lower-order derivative with non-separated type integral boundary conditions[J]. AIMS Mathematics, 2019, 4(1): 112-133. doi: 10.3934/Math.2019.1.112
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