Bashir Ahmad , Juan J.Nieto , Ahmed Alsaedi . EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(6) : 2122 -2130 . DOI: 10.1016/S0252-9602(11)60388-3

[1] Agarwal R P, Benchohra M, Hamani S. Boundary value problems for fractional differential equations. Georgian Math J, 2009, 16: 401–411

[2] Ahmad B, Alsaedi A, Alghamdi B. Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions. Nonlinear Anal Real World Appl, 2008, 9: 1727–1740

[3] Ahmad b, Nieto J J. Existence results for nonlinear boundary value problems of fractional integrodiffer-ential equations with integral boundary conditions. Bound Value Probl, 2009, Art ID 708576

[4] Ahmad B, Nieto J J. Existence of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations. Abstr Appl Anal, 2009, Art ID 494720

[5] Ahmad B, Nieto J J. Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput Math Appl, 2009, 58: 1838–1843

[6] Ahmad B, Sivasundaram S. Existence of solutions for impulsive integral boundary value problems of fractional order. Nonlinear Anal Hybrid Syst, 2010, 4: 134–141

[7] Ahmad B, Sivasundaram S. On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order. Appl Math Comput, 2010, 217: 480–487

[8] Ahmad B. Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations. Appl Math Lett, 2010, 23: 390–394

[9] Ahmad B, Ntouyas S K, Alsaedi A. New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv Differ Equ, 2011, Art ID 107384

[10] Ahmad B, Nieto J J. Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory. Topol Methods Nonlinear Anal, 2010, 35: 295–304

[11] Ahmad B. New results for boundary value problems of nonlinear fractional differential equations with non-separated boundary conditions. Acta Vietnamica, 2011, 36(3): to appear

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

[13] Benchohra M, Graef J R, Hamani S. Existence results for boundary value problems with nonlinear fractional differential equations. Appl Anal, 2008, 87: 851–863

[14] Benchohra M, Hamani S, Ntouyas S K. Boundary value problems for differential equations with fractional order and nonlocal conditions. Nonlinear Anal, 2009, 71: 2391–2396

[15] Boucherif A. Second-order boundary value problems with integral boundary conditions. Nonlinear Anal, 2009, 70: 364–371

[16] Hamani S, Benchohra M, Graef J R. Existence results for boundary value problems with nonlinear fractional inclusions and integral conditions. Electronic J Differ Equ, 2010, 2010(20): 1–16

[17] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Amsterdam: Elsevier Science B V, 2006

[18] Liu X, Jia M, Wu B. Existence and uniqueness of solution for fractional differential equations with integral boundary conditions. E J Qual Theory Diff Equ, 2009, 69: 1–10

[19] Nieto J J. Maximum principles for fractional differential equations derived from Mittag-Leffler functions. Appl Math Lett, 2010, 23: 1248–1251

[20] Podlubny I. Fractional Differential Equations. San Diego: Academic Press, 1999

[21] Sabatier J, Agrawal O P, Machado J A T. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Dordrecht: Springer, 2007

[22] Salem H A H. Fractional order boundary value problem with integral boundary conditions involving Pettis integral. Acta Mathematica Scientia, 2011, 31B(2): 661–672

[23] Samko S G, Kilbas A A, Marichev O I. Fractional Integrals and Derivatives, Theory and Applications. Yverdon: Gordon and Breach, 1993

[24] Smart D R. Fixed Point Theorems. Cambridge: Cambridge University Press, 1980

[25] Zhang S. Existence of solution for a boundary value problem of fractional order. Acta Mathematica Scientia, 2006, 26B(2): 220–228