Quantum difference Langevin equation with multiquantum numbers qderivative nonlocal conditions
Authors
Surang Sitho
 Department of Social and Applied Science, College of Industrial Technology, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.
Sorasak Laoprasittichok
 Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.
Sotiris K. Ntouyas
 Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.
 Nonlinear Analysis and Applied Mathematics (NAAM)Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Jessada Tariboon
 Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.
Abstract
In the present paper, we study a new class of boundary value problems for Langevin quantum difference
equations with multiquantum numbers qderivative nonlocal conditions. Some new existence and uniqueness
results are obtained by using standard fixed point theorems. The existence and uniqueness of solutions is
established by Banach's contraction mapping principle, while the existence of solutions is derived by using
Krasnoselskii's fixed point theorem and LeraySchauder's nonlinear alternative. Examples illustrating the
results are also presented.
Share and Cite
ISRP Style
Surang Sitho, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon, Quantum difference Langevin equation with multiquantum numbers qderivative nonlocal conditions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 34913503
AMA Style
Sitho Surang, Laoprasittichok Sorasak, Ntouyas Sotiris K., Tariboon Jessada, Quantum difference Langevin equation with multiquantum numbers qderivative nonlocal conditions. J. Nonlinear Sci. Appl. (2016); 9(6):34913503
Chicago/Turabian Style
Sitho, Surang, Laoprasittichok, Sorasak, Ntouyas, Sotiris K., Tariboon, Jessada. "Quantum difference Langevin equation with multiquantum numbers qderivative nonlocal conditions." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 34913503
Keywords
 qcalculus
 nonlocal conditions
 Langevin equation
 existence
 fixed point.
MSC
References

[1]
B. Ahmad, Boundary value problems for nonlinear thirdorder qdifference equations, Electron. J. Diff. Equ., 2011 (2011), 7 pages.

[2]
B. Ahmad, A. Alsaedi, S. K. Ntouyas, A study of secondorder qdifference equations with boundary conditions, Adv. Difference Equ., 2012 (2012), 10 pages.

[3]
B. Ahmad, P. Eloe, A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices, Comm. Appl. Nonlinear Anal., 17 (2010), 6980.

[4]
B. Ahmad, J. J. Nieto, Basic theory of nonlinear thirdorder qdifference equations and inclusions, Math. Model. Anal., 18 (2013), 122135.

[5]
B. Ahmad, J. J. Nieto, A. Alsaedi, M. ElShahed, A study of nonlinear Langevin equation involving two fractional orders in different intervals, Nonlinear Anal. Real World Appl., 13 (2012), 599606.

[6]
B. Ahmad, S. K. Ntouyas, Boundary value problems for qdifference inclusions , Abstr. Appl. Anal., 2011 (2011), 15 pages.

[7]
M. H. Annaby, Z. S. Mansour, qFractional Calculus and Equations, SpringerVerlag, Berlin (2012)

[8]
G. Bangerezako, Variational qcalculus, J. Math. Anal. Appl., 289 (2004), 650665.

[9]
W. T. Coffey, Y. P. Kalmykov, J. T. Waldron, The Langevin equation. With applications to stochastic problems in physics, chemistry and electrical engineering: Second edition, World Scientific Publishing Co., Singapore (2004)

[10]
S. I. Denisov, H. Kantz, P. Hänggi, Langevin equation with superheavytailed noise, J. Phys. A, 43 (2010), 10 pages.

[11]
A. Dobrogowska, A. Odzijewicz, Second order qdifference equations solvable by factorization method, J. Comput. Appl. Math., 193 (2006), 319346.

[12]
M. ElShahed, H. A. Hassan, Positive solutions of qdifference equation, Proc. Amer. Math. Soc., 138 (2010), 17331738.

[13]
R. A. C. Ferreira, Nontrivial solutions for fractional qdifference boundary value problems,, Electron. J. Qual. Theory Differ. Equ., 2010 (2010), 10 pages.

[14]
G. Gasper, M. Rahman, Basic hypergeometric series. With a foreword by Richard Askey. Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (1990)

[15]
G. Gasper, M. Rahman, Some systems of multivariable orthogonal qRacah polynomials, Ramanujan J., 13 (2007), 389405.

[16]
A. Granas, J. Dugundji, Fixed Point Theory, SpringerVerlag , New York (2003)

[17]
V. Kac, P. Cheung, Quantum Calculus, SpringerVerlag, New York (2002)

[18]
S. C. Lim, M. Li, L. P. Teo, Langevin equation with two fractional orders, Phys. Lett. A, 372 (2008), 63096320.

[19]
S. C. Lim, L. P. Teo, The fractional oscillator process with two indices, J. Physics A, 42 (2009), 34 pages.

[20]
L. Lizana, T. Ambjörnsson, A. Taloni, E. Barkai, M. A. Lomholt, Foundation of fractional Langevin equation: Harmonization of a manybody problem, Phys. Rev. E, 81 (2010), 8 pages.

[21]
A. Lozinski, R. G. Owens, T. N. Phillips, The Langevin and FokkerPlanck Equations in Polymer Rheology, Handb. Numer. Anal. , 16 (2011), 211303.

[22]
J. Tariboon, S. K. Ntouyas, C. Thaiprayoon, Nonlinear Langevin equation of HadamardCaputo type fractional derivatives with nonlocal fractional integral conditions, Adv. Math. Phys., 2014 (2014), 15 pages.

[23]
M. Uranagase, T. Munakata, Generalized Langevin equation revisited: mechanical random force and selfconsistent structure, J. Phys., 43 (2010), 11 pages