Bekri, ZouaouiErturk, Vedat SuatKumar, Pushpendra2024-01-212024-08-132024-01-212024-08-132021-09-231793962310.1142/S1793962322500118http://10.2.3.109/handle/32116/3373In this research collection, we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form cD q?v(t) - h(t,v(t))=0, 0 ? t ? 1, ?1v(0) + ?1Dqv(0)=v(?1),?2v(1) - ?2Dqv(1) = v(?2), where 1 < ? ? 2, (?1,?2) (0, 1)2, ?i,?i ?(i = 1, 2), h C([0, 1] � ?, ?) and cD q? represents the Caputo-type nonclassical q-derivative of order ?. We use well-known principal of Banach contraction, and Leray-Schauder nonlinear alternative to vindicate the unique solution existence of the given problem. Regarding the applications, some examples are solved to justify our outcomes. � 2022 World Scientific Publishing Company.en-USboundary value problemexistence and uniquenessFractional q -derivativeLeary-Schauder nonlinear alternativeprinciple of Banach contractionArticlehttps://www.worldscientific.com/doi/abs/10.1142/S1793962322500118