TY - JOUR AU - Sitho, Surang AU - Laoprasittichok, Sorasak AU - Ntouyas, Sotiris K. AU - Tariboon, Jessada PY - 2016 TI - Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions JO - Journal of Nonlinear Sciences and Applications SP - 3491--3503 VL - 9 IS - 6 AB - In the present paper, we study a new class of boundary value problems for Langevin quantum difference equations with multi-quantum numbers q-derivative 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 Leray-Schauder's nonlinear alternative. Examples illustrating the results are also presented. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.06.04 DO - 10.22436/jnsa.009.06.04 ID - Sitho2016 ER - TY - JOUR TI - Boundary value problems for nonlinear third-order q-difference equations AU - B. Ahmad JO - Electron. J. Diff. Equ. PY - 2011 DA - 2011// VL - 2011 ID - Ahmad2011 ER - TY - JOUR TI - A study of second-order q-difference equations with boundary conditions AU - B. Ahmad AU - A. Alsaedi AU - S. K. Ntouyas JO - Adv. Difference Equ. PY - 2012 DA - 2012// VL - 2012 ID - Ahmad2012 ER - TY - JOUR TI - A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices AU - B. Ahmad AU - P. Eloe JO - Comm. Appl. Nonlinear Anal. PY - 2010 DA - 2010// VL - 17 ID - Ahmad2010 ER - TY - JOUR TI - Basic theory of nonlinear third-order q-difference equations and inclusions AU - B. Ahmad AU - J. J. Nieto JO - Math. Model. Anal. PY - 2013 DA - 2013// VL - 18 ID - Ahmad2013 ER - TY - JOUR TI - A study of nonlinear Langevin equation involving two fractional orders in different intervals AU - B. Ahmad AU - J. J. Nieto AU - A. Alsaedi AU - M. El-Shahed JO - Nonlinear Anal. Real World Appl. PY - 2012 DA - 2012// VL - 13 ID - Ahmad2012 ER - TY - JOUR TI - Boundary value problems for q-difference inclusions AU - B. Ahmad AU - S. K. Ntouyas JO - Abstr. Appl. Anal. PY - 2011 DA - 2011// VL - 2011 ID - Ahmad2011 ER - TY - BOOK TI - q-Fractional Calculus and Equations AU - M. H. Annaby AU - Z. S. Mansour PB - Springer-Verlag PY - 2012 DA - 2012// CY - Berlin ID - Annaby2012 ER - TY - JOUR TI - Variational q-calculus AU - G. Bangerezako JO - J. Math. Anal. Appl. PY - 2004 DA - 2004// VL - 289 ID - Bangerezako2004 ER - TY - BOOK TI - The Langevin equation. With applications to stochastic problems in physics, chemistry and electrical engineering: Second edition AU - W. T. Coffey AU - Y. P. Kalmykov AU - J. T. Waldron PB - World Scientific Publishing Co. PY - 2004 DA - 2004// CY - Singapore ID - Coffey2004 ER - TY - JOUR TI - Langevin equation with super-heavy-tailed noise AU - S. I. Denisov AU - H. Kantz AU - P. Hänggi JO - J. Phys. A PY - 2010 DA - 2010// VL - 43 ID - Denisov2010 ER - TY - JOUR TI - Second order q-difference equations solvable by factorization method AU - A. Dobrogowska AU - A. Odzijewicz JO - J. Comput. Appl. Math. PY - 2006 DA - 2006// VL - 193 ID - Dobrogowska2006 ER - TY - JOUR TI - Positive solutions of q-difference equation AU - M. El-Shahed AU - H. A. Hassan JO - Proc. Amer. Math. Soc. PY - 2010 DA - 2010// VL - 138 ID - El-Shahed2010 ER - TY - JOUR TI - Nontrivial solutions for fractional q-difference boundary value problems, AU - R. A. C. Ferreira JO - Electron. J. Qual. Theory Differ. Equ. PY - 2010 DA - 2010// VL - 2010 ID - Ferreira2010 ER - TY - BOOK TI - Basic hypergeometric series. With a foreword by Richard Askey. Encyclopedia of Mathematics and its Applications AU - G. Gasper AU - M. Rahman PB - Cambridge University Press PY - 1990 DA - 1990// CY - Cambridge ID - Gasper1990 ER - TY - JOUR TI - Some systems of multivariable orthogonal q-Racah polynomials AU - G. Gasper AU - M. Rahman JO - Ramanujan J. PY - 2007 DA - 2007// VL - 13 ID - Gasper2007 ER - TY - BOOK TI - Fixed Point Theory AU - A. Granas AU - J. Dugundji PB - Springer-Verlag PY - 2003 DA - 2003// CY - New York ID - Granas2003 ER - TY - BOOK TI - Quantum Calculus AU - V. Kac AU - P. Cheung PB - Springer-Verlag PY - 2002 DA - 2002// CY - New York ID - Kac2002 ER - TY - JOUR TI - Langevin equation with two fractional orders AU - S. C. Lim AU - M. Li AU - L. P. Teo JO - Phys. Lett. A PY - 2008 DA - 2008// VL - 372 ID - Lim2008 ER - TY - JOUR TI - The fractional oscillator process with two indices AU - S. C. Lim AU - L. P. Teo JO - J. Physics A PY - 2009 DA - 2009// VL - 42 ID - Lim2009 ER - TY - JOUR TI - Foundation of fractional Langevin equation: Harmonization of a many-body problem AU - L. Lizana AU - T. Ambjörnsson AU - A. Taloni AU - E. Barkai AU - M. A. Lomholt JO - Phys. Rev. E PY - 2010 DA - 2010// VL - 81 ID - Lizana2010 ER - TY - JOUR TI - The Langevin and Fokker-Planck Equations in Polymer Rheology AU - A. Lozinski AU - R. G. Owens AU - T. N. Phillips JO - Handb. Numer. Anal. PY - 2011 DA - 2011// VL - 16 ID - Lozinski2011 ER - TY - JOUR TI - Nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions AU - J. Tariboon AU - S. K. Ntouyas AU - C. Thaiprayoon JO - Adv. Math. Phys. PY - 2014 DA - 2014// VL - 2014 ID - Tariboon2014 ER - TY - JOUR TI - Generalized Langevin equation revisited: mechanical random force and self-consistent structure AU - M. Uranagase AU - T. Munakata JO - J. Phys. PY - 2010 DA - 2010// VL - 43 ID - Uranagase2010 ER -