Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation

• Autorzy: Dou X. , Li Y. , Liu P.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for the problem by using the Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered to the equivalent Fredholm integral equation.

Słowa kluczowe

EN

four-point boundary value problem; Riemann-Liouville fractional derivative; Green's functions; Schauder fixed point theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 3
• Strony: 359--372
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Dou X.

autor

Li Y.

autor

Liu P.

• Yunnan University Department of Mathematics Kunming, Yunnan 650091, P.R. China,

Bibliografia

• [1] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, [in:] North-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam, 2006.
• [2] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
• [3] S.Q. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Electron. J. Differential Equations 36 (2006), 1–12.
• [4] C.Z. Bai, J.X. Fang, The existence of a positive solution for a singular coupled system of a nonlinear fractional differential equations, Appl. Math. Comput. 150 (2004), 611–621.
• [5] B. Ahmad, J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Appl. Math. Comput. 58 (2009), 1838–1843.
• [6] M. Moshiinsky, Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas, Bol. Soc. Mat. Mexicana 7 (1950), 1–25.
• [7] I. Podlubny, Fractional Differential, Mathematics in Science and Engineering, Amsterdam, Elsevier, 2006.
• [8] Z.B. Bai, H.S. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005), 495–505.
• [9] X.W. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett. 22 (2009), 64–69.
• [10] V. Lakshmikantham, S. Leela, Nagumo-type uniqueness result for fractional differential equations, Nonlinear Anal. 71 (2009), 2886–2889.
• [11] A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (1998), 181–186.
• [12] S.Q. Zhang, Existence of positive solution for some class of nonliear fractional differential equations, J. Math. Anal. Appl. 278 (2003), 136–148.
• [13] S. Timoshenko, Theory of Elastic Stability, McGraw-Hill, New York, 1961.