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New classes of evolution differential equations with the Liouville derivative in Banach spaces are studied. Equations are considered on the whole real line and are not endowed by the initial conditions. Using the methods of the Fourier transform theory, we prove the unique solvability in the sense of classical solutions for the equation solved with respect to the Liouville fractional derivative with a bounded operator at the unknown function. This allows us to obtain the analogous result for the equation with a linear degenerate operator at the fractional derivative and with a spectrally bounded pair of operators. Abstract results are applied to obtain new results on the unique solvability of systems of ordinary differential equations, boundary problems to partial differential equations, and systems of equations. [ABSTRACT FROM AUTHOR]

This research aims to explore the potential application of this approach in the production of biosensor chips. The biosensor chip is utilized for the identification and examination of early-stage lung cancer cells. The findings of the optical microscope were corroborated by the field emission scanning electron microscopy, which provided further evidence that the growth of MoS 2 is uniform and that there is minimal disruption in the electrode, hence minimizing the likelihood of an open circuit creation. Furthermore, the bilayer structure of the produced MoS 2 has been validated through the utilization of Raman spectroscopy. A research investigation was undertaken to measure the photoelectric current generated by three various types of clinical samples containing lung cancer cells, specifically the CL1, NCI-H460, and NCI-H520 cell lines. The findings from the empirical analysis indicate that the coefficient of determination (R-Square) for the linear regression model was approximately 98%. Furthermore, the integration of a double-layer MoS 2 film resulted in a significant improvement of 38% in the photocurrent, as observed in the device's performance., Competing Interests: The authors declare no conflict of interest., (© 2024 Optica Publishing Group.)