Browsing by Author "LAKHDARI Abdelghani"

Now showing 1 - 12 of 12
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    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.
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    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.
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    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.
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    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.
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    CORRECTED SIMPSON’S SECOND FORMULA INEQUALITIES ON FRACTAL SET
    (Fractional Differential Calculus, 2024) LAKHDARI Abdelghani
    The aim of this research is to investigate the corrected Simpson’s second formula within the context of local fractional calculus. Firstly, we present a new integral identity that is related to the formula, which enables us to derive several integral inequalities for functions whose local fractional derivatives are generalized (s,P)-convex functions. Lastly, we discuss potential practical applications.
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    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
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    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.
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    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.
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    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.
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    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.
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    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
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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.