[1] R. P. Agarwal, D. O'Regan, S. Stanek, Positive solutions for mixed problems of singular fractional differential equations. *Math. Nachr*. 285 (2012), 27-41.Web of ScienceGoogle Scholar

[2] B. Ahmad, R. P. Agarwal, Some new versions of fractional boundary value problems with slit-strips conditions. *Bound. Value Probl*. 2014 (2014), 175.Web of ScienceGoogle Scholar

[3] B. Ahmad, S. K. Ntouyas, Existence results for higher order fractional differential inclusions with multi-strip fractional integral boundary conditions. Electron. *J. Qual. Theory Differ. Equ*. 2013 (2013), Article No 20, 19 pp.Google Scholar

[4] B. Ahmad, S. K. Ntouyas, A. Alsaedi, A study of nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type multistrip boundary conditions. *Math. Probl. Eng*. 2013 (2013), Article ID 320415, 9 pp.Google Scholar

[5] S. Asghar, T. Hayat, B. Ahmad, Acoustic diffraction from a slit in an infinite absorbing sheet. *Japan J. Indust. Appl. Math*. 13 (1996), 519-532.CrossrefGoogle Scholar

[6] Z. B. Bai, W. Sun, Existence and multiplicity of positive solutions for singular fractional boundary value problems. *Comput. Math. Appl*. 63 (2012), 1369-1381.Google Scholar

[7] D. Baleanu, O. G. Mustafa, R. P. Agarwal, On Lp-solutions for a class of sequential fractional differential equations. *Appl. Math. Comput*. 218 (2011), 2074-2081.Google Scholar

[8] L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. *J. Math. Anal. Appl*. 162 (1991), 494-505.Google Scholar

[9] L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. *Appl. Anal*. 40 (1991), 11-19.CrossrefGoogle Scholar

[10] A. Cabada, G. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. *J. Math. Anal. Appl*. 389 (2012), 403-411.Google Scholar

[11] A. Cernea, On the existence of solutions for nonconvex fractional hyperbolic differential inclusions. *Commun. Math. Anal*. 9, No 1 (2010), 109-120.Google Scholar

[12] Y.-K. Chang, J. J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions. *Math. Comput. Modelling* 49 (2009), 605-609.Google Scholar

[13] K. Deimling, *Multivalued Differential Equations*. Walter De Gruyter, Berlin-New York, 1992.Google Scholar

[14] J. R. Graef, L. Kong, Q. Kong, Application of the mixed monotone operator method to fractional boundary value problems. *Fract. Differ*. Calc. 2 (2011), 554-567.Google Scholar

[15] J. R. Graef, L. Kong, M. Wang, Existence and uniqueness of solutions for a fractional boundary value problem on a graph. *Fract. Calc. Appl. Anal*. 17, No 2 (2014), 499-510; DOI: 10.2478/s13540-014-0182-4; *http://link.springer.com/article/10.2478/s13540-014-0182-4*.CrossrefGoogle Scholar

[16] J. Henderson, A. Ouahab, Fractional functional differential inclusions with finite delay. *Nonlinear Anal*. 70 (2009), 2091-2105.Google Scholar

[17] Sh. Hu, N. Papageorgiou, Handbook of *Multivalued Analysis, Theory*, I. Kluwer, Dordrecht, 1997.Google Scholar

[18] R. A. Hurd, Y. Hayashi, Low-frequency scattering by a slit in a conducting plane. *Radio Sci*. 15 (1980), 1171-1178.CrossrefGoogle Scholar

[19] V. Keyantuo, C. Lizama, A characterization of periodic solutions for time-fractional differential equations in UMD spaces and applications. *Math. Nach*. 284 (2011), 494-506.Google Scholar

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

[21] A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. *Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys*. 13 (1965), 781-786.Google Scholar

[22] S. Liang, J. Zhang, Existence of multiple positive solutions for mpoint fractional boundary value problems on an infinite interval. *Math. Comput. Modelling* 54 (2011), 1334-1346.Google Scholar

[23] S. P. Lipshitz, T. C. Scott, B. Salvy, On the acoustic impedance of baffled strip radiators. *J. Audio Eng. Soc*. 43 (1995), 573-580.Google Scholar

[24] D. O'Regan, Fixed-point theory for the sum of two operators. *Appl. Math. Lett*. 9 (1996), 1-8.CrossrefGoogle Scholar

[25] D. O'Regan, S. Stanek, Fractional boundary value problems with singularities in space variables. *Nonlinear Dynam*. 71 (2013), 641-652.CrossrefWeb of ScienceGoogle Scholar

[26] T. Otsuki, Diffraction by multiple slits. *JOSA A* 7 (1990), 646-652.Google Scholar

[27] W. V. Petryshyn, P. M. Fitzpatric, A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact maps. *Trans. Amer. Math. Soc*. 194 (1974), 1-25.Google Scholar

[28] I. Podlubny, *Fractional Differential Equations. Academic Press*, San Diego, 1999.Google Scholar

[29] J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado (Eds.), *Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering*. Springer, Dordrecht, 2007.Google Scholar

[30] X. Su, Solutions to boundary value problem of fractional order on unbounded domains in a Banach space. *Nonlinear Anal*. 74 (2011), 2844-2852.Google Scholar

[31] Z. Tomovski, R. Hilfer, H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions. *Integral Transforms Spec. Funct*. 21 (2010), 797-814.Google Scholar

[32] G. Wang, S. Liu, L. Zhang, Eigenvalue problem for nonlinear fractional differential equations with integral boundary conditions. *Abstr. Appl. Anal*. 2014 (2014), Article ID 916260, 6 pp.Google Scholar

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