[1] Baleanu, D., Machado, J. A. T., Luo, A. C.-J.:
Fractional Dynamics and Control. Springer, Berlin, 2012.
MR 2905887 |
Zbl 1231.93003
[2] Diethelm, K.:
The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics Vol. 2014, dmlbpublisherSpringer, Berlin, 2010.
MR 2680847 |
Zbl 1215.34001
[3] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J.:
Theory and Applications of Fractional Differential Equations. Vol. 204, Elsevier Science, 2006.
MR 2218073 |
Zbl 1092.45003
[4] Lakshmikantham, V., Leela, S., Vasundhara Devi, J.:
Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, 2009.
Zbl 1188.37002
[5] Miller, K. S., Ross, B.:
An Introduction to the Fractional Calculus and Differential Equations. John Wiley, 1993.
MR 1219954
[6] Michalski, M. W.:
Derivatives of Noninteger Order and Their Applications. Dissertationes Mathematicae 328, Inst. Math., Polish Acad. Sci., 1993.
MR 1247113 |
Zbl 0880.26007
[8] Tarasov, V. E.:
Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media. dmlbpublisherSpringer, 2011.
MR 2796453
[12] Agarwal, R. P., O’Regan, D., Staněk, S.: Positive solutions for mixed problems of singular fractional differential equations. Mathematische Nachrichten 11 (2011), 1–15.
[13] Agarwal, R. P., O’Regan, D., Staněk, S.:
Positive solutions for Dirichlet problems of singular nonlinear frcational differentil equations. J. Math. Anal. Appl. 37 (2010), 57–68.
DOI 10.1016/j.jmaa.2010.04.034
[14] Agarwal, R. P., Benchohra, M., Hamani, S.:
A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta. Appl. Math. 109 (2010), 973–1033.
DOI 10.1007/s10440-008-9356-6 |
MR 2596185 |
Zbl 1198.26004
[15] 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. 35 (2010), 295–304.
MR 2676818 |
Zbl 1245.34008
[16] Bai, Z.:
On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Anal., TMA 72 (2010), 916–924.
MR 2579357 |
Zbl 1187.34026
[20] Wang, J., Zhou, Y.:
Analysis of nonlinear fractional control systems in Banach spaces. Nonlinear Anal., TMA 74 (2011), 5929–5942.
MR 2833364 |
Zbl 1223.93059
[22] Zhou, Y., Jiao, F.:
Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal., RWA 11 (2010), 4465–4475.
MR 2683890 |
Zbl 1260.34017
[23] Zhou, Y., Jiao, F., Li, J.:
Existence and uniqueness for $p$-type fractional neutral differential equations. Nonlinear Anal., TMA 71 (2009), 2724–2733.
MR 2532797 |
Zbl 1175.34082
[25] Fa, K. S.:
Generalized Langevin equation with fractional derivative and long-time correlation function. Phys. Rev. E 73, 061104 (2006), 1–4.
DOI 10.1103/PhysRevE.73.061104
[26] Fa, K. S.:
Fractional Langevin equation and Riemann–CLiouville fractional derivative. Eur. Phys. J. E 24 (2007), 139–143.
DOI 10.1140/epje/i2007-10224-2
[27] Kobolev, V., Romanov, E.:
Fractional Langevin equation to describe anomalous diffusion. Prog. Theor. Phys. Suppl. 139 (2000), 470–476.
DOI 10.1143/PTPS.139.470
[31] Ahmad, B., Nieto, J. J.:
Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions. Int. J. Difference Equ. 2010, ID 649486 (2010), 1–10.
MR 2575288 |
Zbl 1207.34007
[32] Ahmad, B., Eloe, P.:
A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices. Commun. Appl. Nonlinear Anal. 17 (2010), 69–80.
MR 2721923 |
Zbl 1275.34005
[33] Ahmad, B., Nieto, J. J., Alsaedi, A., El-Shahed, M.:
A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Anal., RWA 13 (2012), 599–606.
MR 2846866 |
Zbl 1238.34008
[34] Chen, A., Chen, Y.:
Existence of solutions to nonlinear Langevin equation involving two fractional orders with boundary value conditions. Bound. Value Probl. 2011, ID 516481 (2011), 1–17.
MR 2783108 |
Zbl 1228.34016
[35] Ibrahim, R. W.:
Existence of nonlinear Lane–Emden equation of fractional order. Math. Notes, Miskolc 13 (2012), 39–52.
MR 2954543 |
Zbl 1265.34216
[36] Sandev, T., Tomovski, Ž., Dubbeldam, J. L. A.:
Generalized Langevin equation with a three parameter Mittag–Leffler noise. Physica A 390 (2011), 3627–3636.
DOI 10.1016/j.physa.2011.05.039