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On generalized nonlinear Euler-Bernoulli Beam type equations


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[1] O. P. Agrawal, Formulation of Euler-Lagrange equations for fractional variational problems, J. Math. Anal. Appl., 272 (1) (2002), 368–379.10.1016/S0022-247X(02)00180-4Search in Google Scholar

[2] O. P. Agrawal, Analytical schemes for a new class of fractional differential equations, J. Phys. A: Math. Theor., 40 (2007), 5469–5477.10.1088/1751-8113/40/21/001Search in Google Scholar

[3] O. P. Agrawal, Fractional variational calculus and transversality condition, J. Phys. A, Mathematical and General, 39 (2006), 10375–10384.10.1088/0305-4470/39/33/008Search in Google Scholar

[4] D. Baleanu, J. H. Asad, I. Petras, Fractional order two electric pendulum, Rom. Rep. Phys, 64 (4) (2012), 907–914.Search in Google Scholar

[5] T. Blaszczyk, Analytical and numerical solution of the fractional Euler–Bernoulli beam equation, J. Mech. Mater. Struct., 12 (1) (2017), 23–34.10.2140/jomms.2017.12.23Search in Google Scholar

[6] C. De Coster and P. Habets, Two-Point Boundary Value Problems: Lower and upper solutions, Math. Sci. Eng. Vol 205, Series Editor: C.K. Chui, Elsevier, 2006.Search in Google Scholar

[7] D. Franco, Juan J. Nieto, D. O’Regan, Upper and lower solutions for first order problems with nonlinear boundary conditions, Extracta Math., 18 (2003), 153–160.Search in Google Scholar

[8] A. Guezane-Lakoud, R. Khaldi, and D. F. M. Torres, On a fractional oscillator equation with natural boundary conditions, Progr. Fract. Differ. Appl., 3 (3) (2017), 191–197.10.18576/pfda/030302Search in Google Scholar

[9] D. Jiang, Y. Yang, J. Chu, J, D. O’Regan, The monotone method for Neumann functional differential equations with upper and lower solutions in the reverse order. Nonlinear Anal., Theory Methods Appl., 67 (2007), 2815-2828.10.1016/j.na.2006.09.042Search in Google Scholar

[10] R. Khaldi, A. Guezane-Lakoud, Upper and lower solutions method for higher order boundary value problems, Progr. Fract. Differ. Appl., 3 (1) (2017), 53–57.10.18576/pfda/030105Search in Google Scholar

[11] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.Search in Google Scholar

[12] J. S. Leszczynski, T. Blaszczyk, Modeling the transition between stable and unstable operation while emptying a silo, Granular Matter, 13 (2011), 429–438.10.1007/s10035-010-0240-5Search in Google Scholar

[13] Y. Li, Existence of positive solutions for the cantilever beam equations with fully nonlinear terms, Nonlinear Anal. Real World Appl., 27 (2016), 221–237.10.1016/j.nonrwa.2015.07.016Search in Google Scholar

[14] F. Minhos, T. Gyulov, A.I. Santos, Lower and upper solutions for a fully nonlinear beam equation, Nonlinear Anal., 71 (2009), 281–292.10.1016/j.na.2008.10.073Search in Google Scholar

[15] I. Podlubny, Fractional Differential Equation, Academic Press, Sain Diego, 1999.Search in Google Scholar

[16] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.Search in Google Scholar

eISSN:
2066-7752
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Mathematics, General Mathematics