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Purpose: In this study, first, second, third, and fourth-order derivative spectrophotometric methods utilizing the peak—zero (P—O) and peak-peak (P—P) techniques of measurement were developed for the determination of levofloxacin, norfloxacin, and moxifloxacin. These methods were applied to their combined pharmaceutical dosage form or individually for levofloxacin, norfloxacin, and moxifloxacin. Methods: Linearity was established in the concentration range of 2–20 µg/mL. The procedures are simple, quick, and precise. The developed methods are sensitive, accurate, and cost-effective, demonstrating excellent correlation coefficients (R2 = 0.9998) and mean recovery values ranging from 99.20% to 100.08%, indicating a high level of precision. Results: The developed approach was effectively employed to determine the levofloxacin, norfloxacin, and moxifloxacin content in commercially available pharmaceutical dosages. Conclusions: Statistical analysis and recovery tests confirmed the method's linearity and accuracy. The results suggest that this method can be utilized for routine analysis in both bulk and commercial formulations. The simplicity, accuracy, and cost-effectiveness of the developed methods make them valuable for pharmaceutical analysis. [ABSTRACT FROM AUTHOR]

Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

A coupled system of fractional order Gross-Pitaevskii equations is under consideration in which the time-fractional derivative is given in Caputo sense and the spatial fractional order derivative is of Riesz type. This kind of model may shed light on some time-evolution properties of the rotating two-component Bose¢ Einstein condensates. An unconditional convergent high-order scheme is proposed based on L2-1σ finite difference approximation in the time direction and Galerkin Legendre spectral approximation in the space direction. This combined scheme is designed in an easy algorithmic style. Based on ideas of discrete fractional Grönwall inequalities, we can prove the convergence theory of the scheme. Accordingly, a second order of convergence and a spectral convergence order in time and space, respectively, without any constraints on temporal meshes and the specified degree of Legendre polynomials N. Some numerical experiments are proposed to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with time delay and Riesz space fractional derivatives. The temporal fractional orders in the considered model are taken as 0 < β 0 < β 1 < β 2 < ⋯ < β m < 1 . The problem is first approximated by the L 1 difference method on the temporal direction, and then, the Galerkin–Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. We show that the proposed method is stable and has a convergent order of 2 − β m in time and an exponential rate of convergence in space. We finally provide some numerical experiments to show the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]