s
[1] P. Langevin, On the theory of Brownian motion, Compt. Rend. 146 (1908) 530–533.
[2] N. Wax(Ed.), Selected Papers on Noise and Stochastic Processes, New York, Dover, 1954.
[3] R.M. Mazo, Brownian Motion: Fluctuations, Dynamics, and Applications, Oxford University Press on Demand,
2002.
[4] R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford University Press, 2001.
[5] J. P. Bouchaud and R. Cont, A Langevin approach to stock market fluctuations and crashes, Euro. Phys. J.
B-Condensed Matter Complex Syst. 6(4) (1998) 543–550.
[6] J.G.E.M. Fraaije, A.V. Zvelindovsky, G.J.A. Sevink and N.M. Maurits, Modulated self-organization in complex
amphiphilic systems, Molecular Simul. 25(3-4) (2000) 131–144.
[7] A. Takahashi, Low-Energy Nuclear Reactions and New Energy Technologies Sourcebook, Oxford University Press,
2009.
[8] R. Klages, G. Radons and I. M. Sokolov (Eds.), Anomalous Transport: Foundations and Applications, Weinheim:
Wiley-VCH, 2008.
[9] R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys. 29(1) (1966) 255.
[10] W. T. Coffey and Y. P. Kalmykov, The Langevin Equation with Applications to Atochastic Problems in Physics,
Chemistry and Electrical Engineering, World Scientific, Singapore, 2004.
[11] T. Sandev and A. Tomovski, Langevin equation for a free particle driven by power law type of noises, Phys. Lett.
A 378(1-2) (2014) 1–9.
[12] F. Mainardi, P. Pironi, F. Tampieri, B. Tabarrok and S. Dost, On a generalization of the Basset problem via
fractional calculus, Proc. CANCAM, 95(2) (1995) 836-837.
[13] F. Mainardi and P. Pironi, The fractional langevin equation: Brownian motion revisited, Extracta Math. 10
(1996) 140–154.
[14] E. Lutz, Fractional langevin equation, Fract. Dyn. (2011) 285–305.
[15] O. Baghani, On fractional Langevin equation involving two fractional orders, Commun. Nonlinear Sci. Numerical
Simul. 42 (2017) 675–681.
[16] G. B. Folland, Real Analysis: Modern Techniques and Their Applications, John Wiley and Sons, 2013.
[17] T. Yu, K. Deng and M. Luo, Existence and uniqueness of solutions of initial value problems for nonlinear Langevin
equation involving two fractional orders, Commun. Nonlinear Sci. Numerical Simul. 19(6) (2014) 1661–1668.
[18] H. Fazli and J. Nieto, Fractional Langevin equation with anti-periodic boundary conditions, Chaos, Solit. Fract.
114 (2018) 332–337.
[19] C. Zhai and P. Li, Nonnegative solutions of initial value problems for Langevin equations involving two fractional
orders, Mediter. J. Math. 15(4) (2018) 1[20] Z. Gao, X. Yu and J. Wang, Nonlocal problems for Langevin-type differential equations with two fractional-order
derivatives, Bound. Value Prob. 1 (2016) 52.
[21] J. Wang and X. Li, A uniform method to Ulam-Hyers stability for some linear fractional equations, Mediter. J.
Math. 13(2) (2016) 625–635.
[22] K. Zhao, Impulsive bo undary value problems for two classes of fractional differential equation with two different
Caputo fractional derivatives, Mediter. J. Math. 13(3) (2016) 1033–1050.
[23] B. Ahmad and J. J. Nieto, Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet
boundary conditions, Frac. Diff. Equ. 2010 (2010) Article ID 649486.
[24] B. Ahmad, J. J. Nieto, A. Alsaedi and M. El-Shahed, A study of nonlinear Langevin equation involving two
fractional orders in different intervals, Nonlinear Analysis: Real World Applications, 13(2), (2012), 599–606.
[25] B. Ross(Ed.), The Fractional Calculus and its Application, in: Lecture Notes in Mathematics, Berlin, SpringerVerlag, 1975.
[26] A. Kilbas, H. Srivastava and J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier
B.V, Netherlands, 2006.
[27] I. Podlubny, Fractional Differential Equations, New York: Academic Press, 1999.