Flurbiprofen (FLB) is chemically 2-(3- fluoro-4-phenyl phenyl) propanoic acid. It is a nonsteroidal anti-inflammatory drug (NSAID) used in the treatment of rheumatoid arthritis and osteoarthritis. Oral administration of this drug is associated with severe gastrointestinal side effects like ulceration and gastrointestinal bleeding. The solution to this problem lies in the fact that topically applied NSAIDs are safer than orally. This study aims to prepare different topical semisolid formulation of FLB as cream base (o/w), (w/o) and gel base using different gel-forming agents in different concentrations. Comparing characterization properties in addition to release and diffusion study for all the prepared formulas to select the best on

In this work, we will combine the Laplace transform method with the Adomian decomposition method and modified Adomian decomposition method for semi-analytic treatments of the nonlinear integro-fractional differential equations of the Volterra-Hammerstein type with difference kernel and such a problem which the kernel has a first order simple degenerate kind which the higher-multi fractional derivative is described in the Caputo sense. In these methods, the solution of a functional equation is considered as the sum of infinite series of components after applying the inverse of Laplace transformation usually converging to the solution, where a closed form solution is not obtainable, a truncated number of terms is usually used for numerical

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica^®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between t

In this paper reliable computational methods (RCMs) based on the monomial stan-dard polynomials have been executed to solve the problem of Jeffery-Hamel flow (JHF). In addition, convenient base functions, namely Bernoulli, Euler and Laguerre polynomials, have been used to enhance the reliability of the computational methods. Using such functions turns the problem into a set of solvable nonlinear algebraic system that MathematicaⓇ12 can solve. The JHF problem has been solved with the help of Improved Reliable Computational Methods (I-RCMs), and a review of the methods has been given. Also, published facts are used to make comparisons. As further evidence of the accuracy and dependability of the proposed methods, the maximum error remainder

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

The Population growth and decay issues are one of the most pressing issues in many sectors of study. These issues can be found in physics, chemistry, social science, biology, and zoology, among other subjects.

We introduced the solution for these problems in this paper by using the SEJI (Sadiq- Emad- Jinan) integral transform, which has some mathematical properties that we use in our solutions. We also presented the SEJI transform for some functions, followed by the inverse of the SEJI integral transform for these functions. After that, we demonstrate how to use the SEJI transform to tackle population growth and decay problems by presenting two applications that demonstrate how to use this transform to obtain solutions.

Fin

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

     In this article, we introduce a two-component generalization for a new generalization type of the short pulse equation was recently found by Hone and his collaborators. The coupled of nonlinear equations is analyzed from the viewpoint of Lie’s method of a continuous group of point transformations. Our results show the symmetries that the system of nonlinear equations can admit, as well as the admitting of the three-dimensional Lie algebra. Moreover, the Lie brackets for the independent vectors field are presented. Similarity reduction for the system is also discussed.