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Theory and Modern Applications

Figure 1 | Advances in Difference Equations

Figure 1

From: Formulation of Euler-Lagrange and Hamilton equations involving fractional operators with regular kernel

Figure 1

Numerical evaluation of equation ( 15 ). (a) \(\omega_{1}=0.1\), \(\omega_{2}=1\); (b) \(\omega_{1}=0.6\), \(\omega_{2}=0.9\); (c) \(\omega_{1}=0.9\), \(\omega_{2}=0.4\), and (d) \(\omega_{1}=0.5\), \(\omega_{2}=0.5\). For all cases: a solid line corresponds to \(\gamma=1\), a dash line corresponds to \(\gamma=0.9\), a dot line corresponds to \(\gamma=0.8\), and a dash-dot line corresponds to \(\gamma=0.7\).

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