Existence of Positive Solutions for a Class of Higher-Order Caputo Fractional Differential Equation

Springer Science and Business Media LLC - Tập 14 Số 1 - Trang 157-171 - 2015
Kaihong Zhao1, Ping Gong1
1Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

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Tài liệu tham khảo

Bai, Z.: On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Anal. 72, 916–924 (2010)

Bai, Z., Qiu, T.: Existence of positive solution for singular fractional differential equation. Appl. Math. Comput. 215(7), 2761–2767 (2009)

Bai, Z., Lv, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005)

Chen, F., Zhou, Y.: Attractivity of fractional functional differential equations. Comput. Math. Appl. 62, 1359–1369 (2011)

Chang, Y., Nieto, J.: Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Model. 49, 605–609 (2009)

Goodrich, C.: Existence of a positive solution to a class of fractional differential equations. Appl. Math. Lett. 23, 1050–1055 (2010)

Guo, D., Lakshmikantham, V., Liu, X.: Nonlinear Integral Equations in Abstract Spaces: Mathematics and Its Applications, vol. 373. Kluwer Academic Publishers, Dordrecht (1996)

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

Kilbas, A.A., Trujillo, J.J.: Differential equations of fractional order: methods, results and problems—II. Appl. Anal. 81, 435–493 (2002)

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier B.V, The Netherlands (2006)

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations: North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)

Lakshmikantham, V., Leela, S.: Nagumo-type uniqueness result for fractional differential equations. Nonlinear Anal. 71, 2886–2889 (2009)

Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1993)

Salem, H.: On the existence of continuous solutions for a singular system of nonlinear fractional differential equations. Appl. Math. Comput. 198, 445–452 (2008)

Zhang, X., Liu, L., Wu, Y.: Multiple positive solutions of a singular fractional differential equation with negatively perturbed term. Math. Comput. Model. 55(3), 1263–1274 (2012)

Zhao, Y., Sun, S., Han, Z., et al.: The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 16(4), 2086–2097 (2011)

Zhao, Y., Sun, S., Han, Z., et al.: Positive solutions for boundary value problems of nonlinear fractional differential equations. Appl. Math. Comput. 217(16), 6950–6958 (2011)

Zhang, S.: Positive solutions for boundary value problems of nonlinear fractional differential equations. Electron. J. Differ. Equ. 2006, 1–12 (2006)

Zeidler, E.: Nonlinear Functional Analysis and Its Applications—I: Fixed-Point Theorems. Springer, New York (1986)