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OnFractal–Fractional Simpson-Type Inequalities: New Insights and Refinements of Classical Results
(Licensee MDPI, Basel, Switzerland., 2024-12-10) LAKHDARI Abdelghani
In this paper, we introduce a novel fractal–fractional identity, from which we derive new Simpson-type inequalities for functions whose first-order local fractional derivative exhibits generalized s-convexity in the secondsense. Thisworkintroducesanapproachthatusesthefirst-order local fractional derivative, enabling the treatment of functions with lower regularity requirements compared to earlier studies. Additionally, we present two distinct methodological frameworks, one of which achieves greater precision by refining classical outcomes in the existing literature. The paper concludes with several practical applications that demonstrate the utility of our results.
OnConformable Fractional Milne-Type Inequalities
(Licensee MDPI, Basel, Switzerland., 2024-02-01) LAKHDARI Abdelghani
Building upon previous research in conformable fractional calculus, this study introduces a novel identity. Using this identity as a foundation, we derive a set of conformable fractional Milne type inequalities specifically designed for differentiable convex functions. The obtained results recover someexisting inequalities in the literature by fixing some parameters. These novel contributions aim to enrich the analytical tools available for studying convex functions within the realm of conformable fractional calculus. The derived inequalities reflect an inherent symmetry characteristic of the Milne formula, further illustrating the balanced and harmonious mathematical structure within these frame works. We provide a thorough example with graphical epresentations to support our findings, offering both numerical insights and visual confirmation of the established inequalities
Milne-type inequalities for differentiable s-preinvex functions via Riemann-Liouville fractional integrals
(Faculty of Sciences and Mathematics, University of Niˇs, Serbia, 2024-07-17) LAKHDARI Abdelghani
The objective of this study is to introduce novel fractional Milne-type inequalities for s-preinvex first derivatives. These findings are derived from a fresh fractional identity and offer enhancements to existing outcomes. The study concludes by applying these findings to special means.
Extension of Milne-type inequalities to Katugampola fractional integrals
(BoundaryValueProblems, 2024) LAKHDARI Abdelghani
This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.
Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes
(Journal of Inequalities and Applications, 2025) LAKHDARI Abdelghani
This in-depth study looks at symmetric four-point Newton-Cotes-type inequalities with a focus on error estimates for numerical integration. The precision of these estimates is explored across various classes of functions, including those with bounded variation, bounded derivatives, Lipschitzian derivatives, convex derivatives, and others. The research synthesizes and extends existing knowledge, providing a nuanced understanding of how error bounds depend on the characteristics of integrated functions. Through a systematic review of seminal works, the study contributes to the practical application of numerical integration techniques, offering insight for researchers and practitioners to make informed choices based on the specific features of the functions involved.
Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set
(Licensee MDPI, Basel, Switzerland., 2022-11-29) LAKHDARI Abdelghani
The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result. Using this new identity along with generalized Hölder’s inequality and generalized power mean inequality, we establish some new variants of fractal corrected dual-Simpson-type integral inequalities. Furthermore, some applications for error estimates of quadrature formulas as well as some special means involving arithmetic and p-logarithmic mean are offered to demonstrate the efficacy of our findings.
AnextensionofSchweitzer'sinequality toRiemann-Liouvillefractional integral
(OpenMathematics, 2024-08-26) LAKHDARI Abdelghani
ThisnotefocusesonestablishingafractionalversionakintotheSchweitzerinequality,specifically tailored to accommodate the left-sided Riemann-Liouville fractional integral operator. The Schweitzer inequalityisafundamentalmathematicalexpression,andextendingit tothefractionalrealmholdssignifi canceinadvancingourunderstandingandapplicationsoffractionalcalculus.
An Extension of Left Radau Type Inequalities to Fractal Spaces and Applications
(Licensee MDPI, Basel, Switzerland., 2024-09-23) LAKHDARI Abdelghani
In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension µ is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results.
Anexpandedanalysis of local fractional integral inequalities via generalized (s, P)-convexity
(Journal of Inequalities and Applications, 2024) LAKHDARI Abdelghani
This research aims to scrutinize specific parametrized integral inequalities linked to 1, 2, 3, and 4-point Newton-Cotes rules applicable to local fractional differentiable generalized (s,P)-convex functions. To accomplish this objective, we introduce a novel integral identity and deduce multiple integral inequalities tailored to mappings within the aforementioned function class. Furthermore, we present an illustrative example featuring graphical representations and potential practical applications.
Microstructure, Critical Behavior and Magnetocaloric Properties of Melt-Spun Ni51.82Mn32.37In15.81
(Magnetochemistry, 2022) SOUILAH Saida (Co-Auteur)
Heusler alloy with an atomic composition of Ni51.82Mn32.37In15.81 was prepared by melt spinning from arc-melted ingots. X-ray diffraction, scanning electron microscopy and magnetic measurements were used to study the structural, microstructural and magnetic properties. The crystal structure consists of a mixture of B2 austenite (~50%) and 14M martensite (~50%). The alloy undergoes a second order magnetic transition at a Curie temperature of T A c = 194.2 K. The hysteresis loop reveals the occurrence of exchange bias phenomenon at room temperature. The critical exponents β, γ and δ were estimated using modified Arrott plots, Kouvel–Fisher curves and critical isothermal analysis. The respective values are β = 0.500 ± 0.015, γ = 1.282 ± 0.055 and δ = 3.003 ± 0.002. The critical behaviour in ribbons is governed by the mean field model with a dominated long-range order of ferromagnetic interactions. The maximum entropy change, ∆S max M , for an applied magnetic field of 5 T reaches an absolute value of 0.92 J/kg·K. The experimental results of entropy changes are in good agreement with those calculated using Landau theory.
temperature on the aging of photovoltaic panels: a case study in Algeria
(Energy Reports, 2024) REKIK Badri (Co-Auteur)
various environmental factors. The main elements contributing to this degradation include irradiance, heat, humidity, and cyclic temperature. This paper details the accelerated factors (AFs) calculated from a series of developed equations established to quantify the deterioration mechanisms affecting PV panels. These equations are derived from several models: the Arrhenius model for temperature and irradiance, the Eyring and Peck models for humidity, and the Coffin-Manson model for cyclic temperature. After formulating equations that measure the combined effects of temperature, irradiance, humidity, and cyclic temperature, these equations were employed to analyze the deterioration of the PV panels installed at the Oued El Keberit solar plant in Souk Ahras, Algeria. The investigation revealed that humidity significantly affected the panels during the winter season. In spring, both humidity and irradiance become important factors. During the summer, temperature greatly influences degradation, while lower humidity levels do not significantly affect the panels. In autumn, humidity continues to be a critical factor. According to the obtained results, the highest AF values occur during the summer months, while the lowest AF values are observed in winter. As a result, the PV panels would deteriorate more noticeably during the winter season than in the summer time
Dual Simpson type inequalities for multiplicatively convex functions
(Mathematics Subject Classification, 2023) LAKHDARI Abdelghani; MEFTAH Badreddine (Co-Auteur)
In this paper we propose a new identity for multiplicative differentiable functions, based on this identity we establish a dual Simpson type inequality for multiplicatively convex functions. Some applications of the obtained results are also given
Easy‑handling semi‑floating TiO2‑based aerogel for solar photocatalytic water depollution
(Environmental Science and Pollution Research, 2022) NOUACER Sana
One of the capital issues of photocatalytic technology is how to use photocatalytic materials in real world conditions. Suspension photocatalysts are the most effective, while the handling and recovery of nanoparticles are very challenging and costly. Herein, we report the design of semi-floating aerogel TiO2-based photocatalyst for the oxidation of dyes and photoreduction of Cr(VI). TiO2 aerogel-based photocatalyst was fabricated through in situ polymerization using borax, poly(vinyl alcohol) and polyvinylidene in the presence of H2O2 as a catalyst. Cubic TiO2 aerogel of few centimetres was designed for the photocatalytic tests under solar light irradiation. TiO2 aerogel showed a good photoactivity against the oxidation of three types of dyes and Cr(VI) photoreduction. In terms of dyes, the kinetics of methylene blue oxidation was the fastest as compared to rhodamine B and methyl red, while, a total reduction of Cr(VI) at 10 ppm was obtained within 30 min after the addition of tartaric acid as hole scavenger. TiO2 aerogel can be easily recovered, washed and recycled. TiO2 aerogel can move freely from the top to the deep solution. The semi-floating property could be an advantage to enhance the mass transfer along with bulk solution, as compared to totally floating-based photocatalysts.
On the multiparameterized fractional multiplicative integral inequalities
(Journal of Inequalities and Applications, 2024-04) LAKHDARI Abdelghani (Co-Auteur)
We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.
ON FRACTIONAL BIPARABOLIC INVERSE SOURCE PROBLEM
(Discrete and Continuous Dynamical Systems - Series S, 2024) LAKHDARI Abdelghani
This paper addresses a fractional biparabolic inverse source problem that integrates fractional derivatives with the biparabolic equation to achieve a more precise characterization of anomalous diffusion. We show that this problem is ill-posed according to Hadamard’s sense. To tackle the instability associated with this problem, we apply regularization techniques using the Landweber iterative method. We provide convergence estimates based on a priori information on the exact solution. The paper concludes with numerical experiments that confirm the validity of the proposed theoretical framework.
On multiparametrized integral inequalities via generalized 𝛼-convexity on fractal set
(Mathematical Methods in the Applied Sciences, 2024) LAKHDARI Abdelghani (Co-Auteur)
This article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized 𝛼-convex functions. It introduces a novel extension of the Hermite-Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity. The primary aim is to generalize existing inequalities, highlighting that previously established results can be obtained by setting specific parameters within the main inequalities. The validity of the derived results is demonstrated through an illustrative example, accompanied by 2D and 3D graphical representations. Lastly, the paper discusses potential practical applications of these findings.
An Associated and Nonassociated Flow Rule Comparison for AISI 439- 430TI Forming: Modeling and Experimental Analysis
(Latin American Journal of Solids and Structures, 2021) MATOUGUI Nedjoua (Co-Auteur)
The plastic anisotropy behavior of ferritic stainless steel (FSS) sheets was analyzed and modeled under associated and nonassociated flow rule approaches. Three orthotropic flow functions, known as quadratic Hill48 and nonquadratic (Yld2000-2d and BBC2005), were developed and employed under an associated and nonassociated flow rule hypothesis. For the NAFR based on the initial anisotropy, the mechanical behavior was described by the nonexponential model functions of Yld2000-2d and BBC2005 to predict the directional dependence of mechanical parameters. It provided a considerable advantage in terms of flexibility and good agreement with the experiment. According to the results, the polynomial fit functions of the transverse versus longitudinal true plastic strain curve were used to describe the designated properties corresponding to a selected level of strain. To describe the evolution of anisotropic hardening and potential plastic hardening, seven different loading conditions were considered. The proposed evolutionary non-AFR Yld2000-2d and BBC2005 criteria showed good accuracy in predicting the evolution of hardening yield and Lankford coefficients depending on the plastic deformation.
On fractional biparameterized Newton-type inequalities
(Journal of Inequalities and Applications, 2023) LAKHDARI Abdelghani (Co-Auteur)
In this work, we present a novel biparameterized identity that yields a family of one-, two-, three-, and four-point Newton-type formulas. Subsequently, we establish some new Newton-type inequalities for functions whose first derivatives are α-convex. The investigation is concluded with numerical examples accompanied by graphical representations to substantiate the accuracy of the obtained results.
On Stability of Second Order Pantograph Fractional Differential Equations in Weighted Banach Space
(Fractal and Fractional, 2023) LASKRI Yamina (Co-Auteur)
This work investigates a weighted Banach space second order pantograph fractional differential equation. The considered equation is of second order, expressed in terms of the Caputo– Hadamard fractional operator, and constructed in a general manner to accommodate many specific situations. The asymptotic stability of the main equation’s trivial solution has been given. The primary theorem was demonstrated in a unique manner by employing the Krasnoselskii’s fixed point theorem. We provide a concrete example that supports the theoretical findings.
Parametrized multiplicative integral inequalities
(Advances in Continuous and Discrete Models, 2024) LAKHDARI Abdelghani (Co-Auteur)
In this paper, we introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers’ comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations. Finally, we demonstrate the applicability of our results to special means of real numbers within the realm of multiplicative calculus.

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