ON SOME TOPOLOGICAL PROPERTIES IN GRADUAL NORMED SPACES

In this paper, we have investigated some topological properties of sets in a given gradual normed space. We have stated gradual Hausdorff property and then,we have studied the relationship between gradual closed sets and gradual compact sets. Also, we have given a result about having the closure point for an innite set in a gradual normed space. In the end, we have provided some illustrative examples

On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions

On the Ulam-Hyers-Rassias stability of two structures of discrete fractional three-point boundary value problems: existence theory

We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville and Caputo fractional derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle and the Brouwer fixed point criterion. Moreover, we prove stability, including Hyers-Ulam and Hyers-Ulam-Rassias type results. Finally, some numerical models are provided to illustrate and validate the theoretical results.The Portuguese Foundation for Science and Technology (FCT) and CIDMA. NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation.publishe

2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings

The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a commutative Γ-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ-ideals of Γ-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ-ideals and 2-absorbing Γ-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ-ideal of a Γ-ring and 2-absorbing K-vague Γ-ideal of a Γ-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ-ring of R induced by a 2-absorbing vague weakly complete Γ-ideal of a 2-absorbing Γ-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ-ideal

A novel analytical Aboodh residual power series method for solving linear and nonlinear time-fractional partial differential equations with variable coefficients

The goal of this research is to develop a novel analytic technique for obtaining the approximate and exact solutions of the Caputo time-fractional partial differential equations (PDEs) with variable coefficients. We call this technique as the Aboodh residual power series method (ARPSM), because it apply the Aboodh transform along with the residual power series method (RPSM). It is based on a new version of Taylor's series that generates a convergent series as a solution. Establishing the coefficients for a series, like the RPSM, necessitates the computation of the fractional derivatives each time. As ARPSM just requires the idea of an infinite limit, we simply need a few computations to get the coefficients. This technique solves nonlinear problems without the He's polynomials and Adomian polynomials, so the small size of computation of this technique is the strength of the scheme, which is an advantage over the homotopy perturbation method and the Adomian decomposition method. The absolute and relative errors of five linear and non-linear problems are numerically examined to determine the efficacy and accuracy of ARPSM for time-fractional PDEs with variable coefficients. In addition, numerical results are also compared with other methods such as the RPSM and the natural transform decomposition method (NTDM). Some graphs are also plotted for various values of fractional orders. The results show that our technique is easy to use, accurate, and effective. Mathematica software is used to calculate the numerical and symbolic quantities in the paper

A Study on the Modified Form of Riemann-Type Fractional Inequalities via Convex Functions and Related Applications

In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals of Riemann-type via convex functions. The mean fractional inequalities for functions with convex absolute value derivatives are discovered. Hermite–Hadamard-type fractional inequalities for a symmetric convex function are explored. These results are achieved using a fresh and innovative methodology for the modified form of generalized fractional integrals. Some applications for the results explored in the paper are briefly reviewed.The sixth author is grateful to the Spanish Government and the European Commission for its support through grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE) and to the Basque Government for its support through grants IT1207-19 and IT1555-22

Novel Mean-Type Inequalities via Generalized Riemann-Type Fractional Integral for Composite Convex Functions: Some Special Examples

This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. Then, we establish the main results involving the error estimation of the Hermite–Hadamard inequality for composite convex functions via a generalized Riemann-type fractional integral. Such results are verified by choosing certain composite functions. These results give well-known examples in special cases. The main consequences can generalize many known inequalities that exist in other studies.The sixth author is grateful to the Basque Government for its support through Grants IT1555-22 and KK-2022/00090 and to MCIN/AEI 269.10.13039/501100011033 for Grant PID2021-1235430B-C21/C22

Recent advances in nanocarriers containing Bromelain: In vitro and in vivo studies

Medicinal products of plant origin have long been considered the most affordable and accessible sources to treat different health problems. Bromelain (Br) is a mixture of enzymes derived from pineapple (Ananas comosus L.) with a wide field of applications including medicine, health, food, and cosmetics. Br has various therapeutic effects, such as antimicrobial, antioxidant, anticancer, wound healing, burn treatment, pain relief, anti-inflammatory, inhibition of platelet aggregation, and fibrinolytic activity. On the other hand, most proteins are susceptible to denaturation and structural changes that may reduce their activities. Encapsulation of drug molecules into nanoparticles (NPs) could increase their stability, bioavailability, and overcome other challenges in drug delivery and therapy. This review aimed to highlight various Br nano-formulations approaches, toward the improvement of Br therapeutic efficiency

Approximate numerical algorithms and artificial neural networks for analyzing a fractal-fractional mathematical model

In this paper, an analysis of a mathematical model of the coronavirus is carried out by using two fractal-fractional parameters. This dangerous virus infects a person through the mouth, eyes, nose or hands. This makes it so dangerous that no one can get rid of it. One of the main factors contributing to increasing infections of this deadly virus is crowding. We believe that it is necessary to model this effect mathematically to predict the possible outcomes. Hence, the study of neural network-based models related to the spread of this virus can yield new results. This paper also introduces the use of artificial neural networks (ANNs) to approximate the solutions, which is a significant contribution in this regard. We suggest employing this new method to solve a system of integral equations that explain the dynamics of infectious diseases instead of the classical numerical methods. Our study shows that, compared to the Adams-Bashforth algorithm, the ANN is a reliable candidate for solving the problems

Children’s and adolescents’ rising animal-source food intakes in 1990–2018 were impacted by age, region, parental education and urbanicity

Animal-source foods (ASF) provide nutrition for children and adolescents’ physical and cognitive development. Here, we use data from the Global Dietary Database and Bayesian hierarchical models to quantify global, regional and national ASF intakes between 1990 and 2018 by age group across 185 countries, representing 93% of the world’s child population. Mean ASF intake was 1.9 servings per day, representing 16% of children consuming at least three daily servings. Intake was similar between boys and girls, but higher among urban children with educated parents. Consumption varied by age from 0.6 at <1 year to 2.5 servings per day at 15–19 years. Between 1990 and 2018, mean ASF intake increased by 0.5 servings per week, with increases in all regions except sub-Saharan Africa. In 2018, total ASF consumption was highest in Russia, Brazil, Mexico and Turkey, and lowest in Uganda, India, Kenya and Bangladesh. These findings can inform policy to address malnutrition through targeted ASF consumption programmes.publishedVersio