Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation.

In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method.

5-Chloro-1,3-dimethyl-1H-pyrazole-4-carbaldehyde.

In the title compound, C(6)H(7)ClN(2)O, the mol-ecules are situated on mirror planes, so H atoms of two methyl groups were treated as rotationally disordered over two orientations each. The crystal packing exhibits weak inter-molecular C-H⋯O inter-actions and short Cl⋯N contacts of 3.046 (2) Å.

5-(2,4-Dichloro-phen-oxy)-1,3-dimethyl-1H-pyrazole-4-carbaldehyde.

In the title mol-ecule, C(12)H(10)Cl(2)N(2)O(2), the benzene and pyrazole rings form a dihedral angle of 72.8 (3)°. In the crystal, weak inter-molecular C-H⋯O hydrogen bonds link the mol-ecules into chains along [01[Formula: see text]].

(E)-3-Methyl-5-(4-methyl-phen-oxy)-1-phenyl-1H-pyrazole-4-carbaldehyde O-[(2-chloro-1,3-thia-zol-5-yl)meth-yl]oxime.

In the title compound, C(22)H(19)ClN(4)O(2)S, the planes of the benzene ring, the substituted phenyl ring and the thia-zole ring make dihedral angles of 18.4 (3), 88.9 (2) and 63.

(E)-1-Methyl-5-(3-methyl-4-chloro-phen-oxy)-3-trifluoro-meth-yl-1H-pyrazole-4-carbaldehyde O-acetyl-oxime.

In the title mol-ecule, C(15)H(13)ClF(3)N(3)O(3), the pyrazole and benzene rings form a dihedral angle of 77.6 (3)°. In the crystal, mol-ecules related by translation along the a axis are linked into chains via C-H⋯O hydrogen bonds.