Abstract
In this chapter, we investigate the existence of solutions for nonlinear Langevin equations and inclusions involving Hadamard-Caputo type fractional derivatives equipped with nonlocal fractional integral conditions. We also study a coupled system of nonlinear Langevin equations with uncoupled boundary conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahmad, B., and P.W. Eloe. 2010. A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices. Communications on Applied Nonlinear Analysis 17:69–80.
Ahmad, B., J.J. Nieto, A. Alsaedi, and M. El-Shahed. 2012. A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Analysis: Real World Applications 13:599–606.
Castaing, C., and M. Valadier. 1977. Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580. Berlin-Heidelberg-New York: Springer.
Coffey, W.T., Yu.P. Kalmykov, and J.T. Waldron. 2004. The Langevin Equation, 2nd ed. Singapore: World Scientific.
Denisov, S.I., H. Kantz, and P. Hänggi. 2010. Langevin equation with super-heavy-tailed noise. Journal of Physics A: Mathematical and Theoretical 43:10. Art. ID 285004.
Gambo, Y.Y., F. Jarad, D. Baleanu, and T. Abdeljawad. 2014. On Caputo modification of the Hadamard fractional derivative. Advances in Difference Equations 2014:10.
Lim, S.C., M. Li, and L.P. Teo. 2008. Langevin equation with two fractional orders. Physics Letters A 372:6309–6320.
Lim, S.C., and L.P. Teo. 2009. The fractional oscillator process with two indices. Journal of Physics A: Mathematical and Theoretical 42:34. Art. ID 065208.
Lizana, L., T. Ambjörnsson, A. Taloni, E. Barkai, and M.A. Lomholt. 2010. Foundation of fractional Langevin equation: Harmonization of a many-body problem. Physical Review E 81:8. Art. ID 051118.
Lozinski, A., R.G. Owens, and T.N. Phillips. 2011. The Langevin and Fokker-Planck Equations in Polymer Rheology. Handbook of Numerical Analysis, vol. 16(C), pp. 211–303.
Ntouyas, S.K., and J. Tariboon. 2016. Fractional integral problems for Hadamard-Caputo fractional Langevin differential inclusions. Journal of Applied Mathematics and Computing 51:13–33.
Sudsutad, W., S.K. Ntouyas, and J. Tariboon. 2015. Systems of fractional Langevin equation via Riemann-Liouville and Hadamard types and their fractional integral conditions. Advances in Difference Equations 2015:235.
Tariboon, J., S.K. Ntouyas, and Ch. Thaiprayoon. 2014. Nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. Advances in Mathematical Physics 2014:Article ID 372749:15 pp.
Uranagase, M., and T. Munakata. 2010. Generalized Langevin equation revisited: mechanical random force and self-consistent structure. Journal of Physics A: Mathematical and Theoretical 43:11. Art. ID 455003.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Ahmad, B., Alsaedi, A., Ntouyas, S.K., Tariboon, J. (2017). Nonlinear Langevin Equation and Inclusions Involving Hadamard-Caputo Type Fractional Derivatives. In: Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-319-52141-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-52141-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52140-4
Online ISBN: 978-3-319-52141-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)