In this paper, we propose an innovative approach to determine the approximate solution of the coupled time-fractional Keller-Segel (K-S) model. We use the fractional complex transform (FCT) to switch the model into its differential partner, and then, the homotopy perturbation method (HPM) is introduced to tackle its nonlinear elements using He’s polynomials. This two-scale theory helps to define the physical meaning of the FCT for the solution of the K-S model. Some examples are illustrated to show that the proposed scheme presents the significant results. The considerable findings show that this strategy does not require any assumptions and also reduces the massive computations without imposing any constraints. This technique is also suitable in functional studies of fractal calculus due to its powerful and robust support for nonlinear problems.

In this study, we propose a new iterative scheme (NIS) to investigate the approximate solution of the fourth-order parabolic partial differential equations (PDEs) that arises in transverse vibration problems. We introduce the Mohand transform as a new operator that is very easy to implement coupled with the homotopy perturbation method. This NIS is capable of reducing the linearization, perturbation, and restrictive assumptions that ruin the nature of the numerical problems. Some numerical examples are demonstrated to legitimate the accuracy and authenticity of this NIS. The computational results are obtained in the shape of a series that converges only after a few iterations. The comparison of the graphical representations shows that NIS is a very simple but also an effective approach for other numerical problems involving complex variables.

This paper introduces and studies a novel class of G−open sets in G−metrizable spaces, known as G(Θ)-open sets. The connections between this form and the other known sets are explained. The concepts of the frontier, closure, and interior operators are provided via G(Θ)-open sets. Keywords: novel classes- G−open sets- G−metrizable spaces بعض الفئات الجديدة من المجموعات المفتوحة- G في الفضاءات القابلة للقياس- G الملخص تقدم هذه الورقة وتدرس فئة جديدة من المجموعات المفتوحة- G في الفضاءات القابلة للقياس- G، والمعروفة باسم المجموعات المفتوحة- G(Θ). يتم شرح الارتباطات بين هذا الشكل والمجموعات الأخرى المعروفة. يتم توفير مفاهيم المشغلات الحدودية والإغلاقية والداخلية من خلال المجموعات المفتوحة- G(Θ). الكلمات المفتاحية: الفئات الجديدة- المجموعات المفتوحة- G-الفضاءات القابلة للقياس- G.

By using ω−open sets in this work, we introduce and study some new classes of open sets in topological spaces that are finer than those of open sets. The continuity via these classes will be introduced and studied.

The objective of this paper is to present and examine these concepts within the context of grill topolog ical spaces, introducing novel categories of θ(∆)−closed sets and θ(∆)−continuous functions specific to grilltopological spaces.