The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann–Stieltjes integral boundary condition

Metzler, 1995, Relaxation in filled polymers: a fractional calculus approach, J. Chem. Phys., 103, 7180, 10.1063/1.470346 Bouchand, 1990, Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications, Phys. Rep., 195, 127, 10.1016/0370-1573(90)90099-N Nonnenmacher, 1995, On the Riemann–Liouville fractional calculus and some recent applications, Fractals, 3, 557, 10.1142/S0218348X95000497 Podlubny, 2002, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calc. Appl. Anal., 5, 367 Hilfer, 2000 Ahmad, 2009, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl., 58, 1838, 10.1016/j.camwa.2009.07.091 Goodrich, 2011, Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions, Comput. Math. Appl., 61, 191, 10.1016/j.camwa.2010.10.041 Goodrich, 2012, Positive solutions to boundary value problems with nonlinear boundary conditions, Nonlinear Anal., 75, 417, 10.1016/j.na.2011.08.044 Goodrich, 2011, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl., 62, 1251, 10.1016/j.camwa.2011.02.039 Yang, 2010, Positive solutions for third-order Sturm–Liouville boundary value problems with p-Laplacian, Comput. Math. Appl., 59, 2059, 10.1016/j.camwa.2009.12.011 Wang, 2009, Positive solutions for three-point boundary value problems of nonlinear fractional differential equations with p-Laplacian, Far East J. Appl. Math., 37, 33 Wang, 2010, Upper and lower solutions method for a class of singular fractional boundary value problems with p-Laplacian operator, Abstr. Appl. Anal., 12, 2010 Chai, 2012, Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator, Bound. Value Probl., 2012, 18, 10.1186/1687-2770-2012-18 Bai, 2005, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311, 495, 10.1016/j.jmaa.2005.02.052 Webb, 2009, Nonlocal conjugate type boundary value problems of higher order, Nonlinear Anal., 71, 1933, 10.1016/j.na.2009.01.033 Zhang, 2012, Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations, Appl. Math. Lett., 25, 555, 10.1016/j.aml.2011.09.058 Miller, 1993 Nieto, 2013, Positive solutions of a fractional thermostat model, Bound. Value Probl., 2013, 10.1186/1687-2770-2013-5 Ding, 2013, Waveform relaxation methods for fractional functional differential equations, Fract. Calc. Appl. Anal., 16, 573, 10.2478/s13540-013-0037-4 Ahmad, 2013, Boundary value problems for a class of sequential integrodifferential equations of fractional order, J. Funct. Spaces Appl., 2013, 10.1155/2013/149659 Wu, 2013, Eigenvalue of fractional differential equations with p-Laplacian operator, Discrete Dyn. Nat. Soc., 2013, 10.1155/2013/137890 Li, 2013, Positive solution for the nonlinear Hadamard type fractional differential equation with p-Laplacian, J. Funct. Spaces Appl., 2013, 10.1155/2013/951643 Jesus, 2008, Fractional electrical impedances in botanical elements, J. Vibr. Control, 14, 1389, 10.1177/1077546307087442 Zhang, 2012, The eigenvalue problem for a singular higher fractional differential equation involving fractional derivatives, Appl. Math. Comput., 218, 8526 Petrovic, 2005, On a mathematical model of a human root dentin, Demonstratio Math., 21, 125 Zhang, 2012, Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives, Appl. Math. Comput., 219, 1420 Ahmed, 2010, On fractional order models for Hepatitis C, Nonlinear Biomed. Phys., 4, 1, 10.1186/1753-4631-4-1 X. Zhang, L. Liu, B. Wiwatanapataphee, Y. Wu, Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives, Abstr. Appl. Anal. vol. 2012 (2012), Article ID 512127, 16p. Perelson, 1993, Dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114, 81, 10.1016/0025-5564(93)90043-A Zhang, 2013, The uniqueness of positive solution for a singular fractional differential system involving derivatives, Commun. Nonlinear Sci. Numer. Simul., 18, 1400, 10.1016/j.cnsns.2012.08.033 Zhang, 2012, Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math. Comput. Model., 55, 1263, 10.1016/j.mcm.2011.10.006 Perelson, 1993, Dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114, 81, 10.1016/0025-5564(93)90043-A Zhang, 2013, The iterative solutions of nonlinear fractional differential equations, Appl. Math. Comput., 219, 4680 Arafa, 2012, Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection, Nonlinear Biomed. Phys., 6, 1, 10.1186/1753-4631-6-1