This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

The present report depicts a convenient route for the synthesis of new N-Mannich bases from Ciprofloxacin (CP) drug. The synthetic route started from the reaction CP drug with 2-mercaptobenzimidazole to give compound [A], the N-Mannich bases analogs of CP [A1-A8] were prepared by the reaction of CP derivative [A] with primary and secondary amine derivatives. The structure of the analogs was confirmed by spectral (1 HNMR and FTIR) and analytical data. This study also includes calculations of total energy and electrostatic potential. In addition, this research aimed to determine the effects of CP derivatives on the activity of various transferase enzymes in sera, such as serum glutamic-oxaloacetic transaminase (GOT) and Glutamate Pyruvate Tra

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