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In our paper, we computed some new characterizations due to an alternative modified frameN⃗,C⃗,W⃗$\left\{ \overrightarrow {N}, \overrightarrow {C}, \overrightarrow {W}\right\}$in Euclidean 3-space and we get general differential equation characterizations of a space curve due to the vectorsN⃗,C⃗,W⃗$ \overrightarrow {N}, \overrightarrow {C}, \overrightarrow {W}$. Furthermore, we investigated some differential equations characterizations of the harmonic and harmonic 1-type curves.

international journal of nonlinear sciences and numerical simulation

Some new characterizations of a space curve due to a modified frame                  N     ⃗       ,            C     ⃗       ,            W     ⃗              $\left\{ \overrightarrow {N},\; \overrightarrow {C},\; \overrightarrow {W}\right\}$          in Euclidean 3-space