Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity.

Symmetry plays an essential role in determining the correct methods for the oscillatory properties of solutions to differential equations. This paper examines some new oscillation criteria for unbounded solutions of third-order neutral differential equations of the form ${(r_2(\varsigma ){({(r_1(\varsigma ){(z^{\prime }(\varsigma ))}^{{\beta }_1})}^{\prime })}^{{\beta }_2})}^{\prime }$ + ${\displaystyle \sum _{i=1}^n}{q}_i(\varsigma )x^{{\beta }_3}({\varphi }_i(\varsigma ))=0.$ New oscillation results are established by using generalized Riccati substitution, an integral average technique in the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

In this study, we employ the dislocated metric space stability result of an equation with one variable function to prove different stabilities of a two variable equation involving rational function in the codomain of complete dislocated quasi-metric spaces. We also extend the stabilities by taking different upper bounds.

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.

Operations research is the applied side of mathematics, and since its inception it has helped to improve the performance of many systems that used its methods in its workflow, one of the methods of operations research is the theory of queues that have been used in many aspects of life, especially the aspects that are directly related to customer service, and the goal is to serve the customer as soon as possible and at the lowest cost, which prompted many researchers to provide the research and studies that can be applied in systems that have a queue.These studies showed good results, from these studies this research is presented to find the optimal value of the service rate in the unlimited model according to classical logic, we present in this research a study to find the relationship through which we get the optimal value of the service rate using neutrosophic logic and this study is an expansion of the study according to classical logic, through the two studies The great benefit we get when using neutrosophic logic and neutrosophic values in operations research topics is demonstrated.