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Impulsively hybrid fractional quantum Langevin equation with boundary conditions involving Caputo qk-fractional derivatives

Author

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  • Sudsutad, Weerawat
  • Ahmad, Bashir
  • Ntouyas, Sotiris K.
  • Tariboon, Jessada

Abstract

We obtain some existence and uniqueness results for an impulsively hybrid fractional quantum Langevin (qk-difference) equation involving a new qk-shifting operator aΦqk(m)=qkm+(1−qk)a and supplemented with non-separated boundary conditions containing Caputo qk-fractional derivatives. Our first result, relying on Banach’s fixed point theorem, is concerned with the existence of a unique solution of the problem. The existence results are established by means of Leray–Schauder nonlinear alternative and a fixed point theorem due to O’Regan. We construct some examples for the applicability of the obtained results. The paper concludes with interesting observations.

Suggested Citation

  • Sudsutad, Weerawat & Ahmad, Bashir & Ntouyas, Sotiris K. & Tariboon, Jessada, 2016. "Impulsively hybrid fractional quantum Langevin equation with boundary conditions involving Caputo qk-fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 47-62.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:47-62
    DOI: 10.1016/j.chaos.2016.05.002
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    References listed on IDEAS

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    1. Jessada Tariboon & Sotiris K. Ntouyas & Chatthai Thaiprayoon, 2014. "Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-15, November.
    2. Ahmad, Bashir & Ntouyas, Sotiris K. & Tariboon, Jessada & Alsaedi, Ahmed & Alsulami, Hamed H., 2016. "Impulsive fractional q-integro-difference equations with separated boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 199-213.
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