In the present study, a novel fractional Meyer neuro-evolution-based intelligent computing solver (FMNEICS) is presented for numerical treatment of doubly singular multi-fractional Lane–Emden system (DSMF-LES) using combined heuristics of Meyer wavelet neural networks (MWNN) optimized with global search efficacy of genetic algorithms (GAs) and sequential quadratic programming (SQP), i.e., MWNN-GASQP. The design of novel FMNEICS for DSMF-LES is presented after derivation from standard Lane–Emden equation, and the singular points and shape factors along with fractional-order terms are analyzed. The MWNN modeling strength is used to represent the system model DSMF-LES in the mean-squared error-based merit function and optimization of the networks is carried out with integrated optimization ability of GASQP. The verification, validation, and perfection of the FMNEICS for three different cases of DSMF-LES are established through comparative studies from reference solutions on convergence, robustness, accuracy, and stability measures. Moreover, the observations through the statistical analysis further authenticate the worth of proposed fractional MWNN-GASQP-based stochastic solver.

FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system

In this work, an improvement of Holder-McCarty inequality is established. Based on that, several refinements of the generalized mixed Schwarz inequality are obtained. Consequently, some new numerical radius inequalities are proved. New inequalities for numerical radius of $n\times n$ matrix of Hilbert space operators are proved as well. Some refinements of some earlier results were proved in literature are also given. Some of the presented results are refined and it shown to be better than earlier results were proved in literature.

Numerical radius inequalities for Hilbert Space Operators

Let G be a monoid with identity e, and let R be a G-graded commutative ring. Here we study the graded prime submodules of a G-graded R-module. A number of results concerning of these class of submodules are given.

On graded prime submodules

Let G be a multiplicative group. Let R be a G-graded commutative ring and M a G-graded R-module. Various properties of graded prime submodules and graded primary submodules of M are discussed. We have also discussed the graded radical of graded submodules of multiplication graded R-modules.

/pdf/on-graded-prime-and-primary-submodules-44wxc364v5.pdf

On graded prime and primary submodules

Numerical radius inequalities and its applications in estimation of zeros of polynomials

Let G be a group and R be a G-graded commutative ring, i.e., R = g2G Rg and RgRhRgh for all g, h2G. In this paper, we study the graded primary ideals and graded primary G-decomposition of a graded ideal.

https://journals.tubitak.gov.tr/math/issues/mat-04-28-3/mat-28-3-2-0301-6.pdf

On Graded Primary Ideals

The latent potentialities and applications of fractional calculus present a mathematical challenge to establish its theoretical framework. One of these challenges is to have a compact and self-contained fractional power series representation that has a wider application scope and allows studying analytical properties. In this letter, we introduce a new more general form of fractional power series expansion, based on the Caputo sense of fractional derivative, with corresponding convergence property. In order to show the functionality of the proposed expansion, we apply the corresponding iterative fractional power series scheme to solve several fractional (integro-)differential equations.

Theory and applications of a more general form for fractional power series expansion

In this paper, we introduce and study graded 2-absorbing and graded weakly 2-absorbing ideals of a graded ring which are different from 2-absorbing and weakly 2-absorbing ideals. We give some properties and characterizations of these ideals and their homogeneous components. We investigate graded (weakly) 2-absorbing ideals of $R_{1}\times R_{2}$ where $R_{1}$ and $R_{2}$ are two graded rings.

/pdf/on-graded-2-absorbing-and-graded-weakly-2-absorbing-ideals-ia1gtzwhqc.pdf

On graded 2-absorbing and graded weakly 2-absorbing ideals

Let G be a group with identity e. Let R be a G-graded commutative ring and M be a graded R-module. In this paper, we introduce the concepts of graded 2-absorbing and weakly graded 2-absorbing submodules and study some of their properties.

On graded 2-absorbing and weakly graded 2-absorbing submodules

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce several results concerning graded classical prime submodules. For example, we give a characterization of graded classical prime submodules. Also, the relations between graded classical prime and graded prime submodules of M are studied.

Khaldoun Al-Zoubi

Papers

On Graded Primary Ideals

Theory and applications of a more general form for fractional power series expansion

On graded 2-absorbing and graded weakly 2-absorbing ideals

On graded 2-absorbing and weakly graded 2-absorbing submodules

On graded classical prime and graded prime submodules