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

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

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 47-62

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.

Keywords: Quantum calculus; Impulsive fractional qk-difference equations; Existence; Uniqueness; Fixed point (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:47-62

DOI: 10.1016/j.chaos.2016.05.002

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