This study describes the synthesis, theoretical investigations, and photocatalytic degradational properties of a new (pyrazine)(meso-tetrakis(4-tert-methoxyphenyl)-porphyrinato)-cadmium (II) ([Cd(TMPP)-Pyz]) complex (1). The new penta-coordinated Cd^II porphyrin complex (1) was characterized by various spectroscopic techniques, including FT-IR, NMR, UV-visible absorption, fluorescence emission, and singlet oxygen, while its molecular structure was studied using single crystal X-ray diffraction. The UV–Vis spectroscopic study highlighted the redshift of the absorption bands after the insertion of the Cd(II) metal ion into the TMPP ring. The co-coordination of the pyrazine axial ligand enhanced this effect. A fluorescence emission spectroscopic study showed a significant blueshift in the Q bands, accompanied by a decrease in the fluorescence emission intensity and quantum yields of Φ_f = 0.084, Φ_f = 0.06 and Φ_f = 0.03 for H₂-TMPP free-base porphyrin, [Cd(TMPP)] and [Cd(TMPP)(Pyz)] (1) respectively. Singlet oxygen revealed that the H₂-TMPP porphyrin produced the most efficient singlet oxygen quantum yield of (Φ_Δ = 0.73) compared to [CdTMPP] (Φ_Δ = 0.57) and [Cd(TMPP)(Pyz)] (1) (Φ_Δ = 0.13). In the crystal lattice, the [Cd(TMPP)Pyz] was stabilized through non-covalent intermolecular interactions (NCI), such as the hydrogen bonds C-H···N and C-H···Cg. Additionally, crystal explorer software was then utilized to measure the quantitative analysis of the intermolecular interactions in the unit cell of the crystal structure and established that the C-H···π interaction dominated. The Natural bond orbital (NBO) analysis revealed that each molecule is stabilized by hyperconjugation and charge delocalization. As a photocatalyst, the coordination complex 1 showed excellent photocatalytic activity toward the degradation of Levafix Blue CA reactive dye (i.e., dye photo-degradation of 80%).

In this paper, the existence of a unique solution is established for a coupled system of Langevin fractional problems of $\mathsf{\psi }$-Caputo fractional derivatives with generalized slit-strip-type integral boundary conditions and impulses using the Banach contraction principle. We also find at least one solution to the aforementioned system using some assumptions and Schaefer’s fixed point theorem. After that, Ulam–Hyers stability is discussed. Finally, to provide additional support for the main results, pertinent examples are presented.

The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q-fractional Langevin differential equation with q-fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed q-fractional Langevin differential equation using the Banach contraction principle and Schaefer’s fixed-point theorem. We also elaborate on different kinds of Ulam stability. The theoretical outcomes are verified by examples.