In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

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In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.

Drug solubility and dissolution remain a significant challenge in pharmaceutical formulations. This study aimed to formulate and evaluate repanglinide (RPG) nanosuspension-based buccal fast-dissolving films (BDFs) for dissolution enhancement. RPG nanosuspension was prepared by the antisolvent-precipitation method using multiple hydrophilic polymers, including soluplus®, polyvinyl alcohol, polyvinyl pyrrolidine, poloxamers, and hydroxyl propyl methyl cellulose. The nanosuspension was then directly loaded into BDFs using the solvent casting technique. Twelve formulas were prepared with a particle size range of 81.6-1389 nm and PDI 0.002-1 for the different polymers. Nanosuspensions prepared with soluplus showed a favored mean particle size o

Position control of servo motor systems is a challenging task because of inevitable factors such as uncertainties, nonlinearities, parametric variations, and external perturbations. In this article, to alleviate the above issues, a practical adaptive fast terminal sliding mode control (PAFTSMC) is proposed for better tracking performance of the servo motor system by using a state observer and bidirectional adaptive law. First, a smooth-tangent-hyperbolic-function-based practical fast terminal sliding mode control (PFTSM) surface is designed to ensure not only fast finite time tracking error convergence but also chattering reduction. Second, the PAFTSMC is proposed for the servo motor, in which a two-way adaptive law is designed to further s