Yazar "Sarikaya, Mehmet Zeki" seçeneğine göre listele

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    A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves
    (Vilnius Gediminas Tech Univ, 2025) Lamamri, Abdelkader; Gouari, Yazid; Dahmani, Zoubir; Rakah, Mahdi; Sarikaya, Mehmet Zeki
    In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The existence and uniqueness of solutions for the class of systems is proved by applying Banach contraction principle. The existence of at least one solution is then accomplished by applying Schauder fixed point theorem. The Ulam Hyers stability, with a limiting-case example, is also discussed. In a second part of our work, we use the tanh method to obtain a new travelling wave solution for the coupled system of Burgers using time and space Khalil derivatives. By bridging these two aspects, we aim to present an understanding of the system's behaviour.
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    EXISTENCE RESULTS FOR A HYBRID SYSTEM OF MIXED DIFFERENTIAL EQUATIONS WITH SEQUENTIAL FRACTIONAL DERIVATIVES
    (Univ Nis, 2025) Benmehidi, Hammou; Sarikaya, Mehmet Zeki; Dahmani, Zoubir
    In this paper, we focus on the study of a hybrid system of sequential type that incorporates both Caputo and Hadamard fractional derivatives. Our approach leverages the fixed point principle to derive novel results concerning the existence and uniqueness of solutions to this system. Additionally, we establish further results by employing Schaefer's fixed point theorem, which allows us to extend the applicability of our findings. To illustrate the practical relevance and application of our theoretical results, we also provide a detailed example at the conclusion of the paper. At the end, an example is given.
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    Extensions of Simpson's Inequality via Nonnegative Weight Functions and Fractional Operators
    (Wiley, 2025) Ogunmez, Hasan; Sarikaya, Mehmet Zeki
    In this paper, we present a new version of Simpson-type inequalities for differentiable functions defined on a subinterval of the positive real axis. The approach involves a nonnegative integrable weight function and provides an identity that refines the classical Simpson inequality by incorporating the first derivative of the function. A key aspect of this work is the inclusion of the Riemann-Liouville fractional integral, through which we derive specific inequalities that extend the classical framework. In certain cases, our results reduce to the well-known Simpson inequality, demonstrating the generality and flexibility of the method.MSC2020 Classification: 26A09, 26D10, 26D15, 33E20
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    Hardy Type Inequalities for Convex Functions
    (Prof. Dr. Mehmet Zeki SARIKAYA, 2023) Sarikaya, Mehmet Zeki
    In this article, we aim to extend the scope of Hardy type inequalities by exploring their applicability to convex functions. We present various types of new Hardy integral inequalities for convex functions, which can be applied in diverse scenarios. Additionally, we provide several practical applications of these inequalities. © 2024 Elsevier B.V., All rights reserved.
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    MILNE-TYPE INEQUALITIES FOR h- CONVEX FUNCTIONS
    (Michigan State Univ Press, 2024) Benaissa, Bouharket; Sarikaya, Mehmet Zeki
    Milne-type inequalities for h- convex functions involving conformable operators are established. Additionally, new results are presented that generalize various known inequalities.
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    New (α, β)-order pre-Gruss fractional integral inequalities and applications for CRV
    (Univ Nis, Fac Sci Math, 2025) Dahmani, Zoubir; Sarikaya, Mehmet Zeki
    In this paper, we employ Riemann-Liouville fractional integrals to derive two primary integral findings concerning the alpha- pre-Gruss inequality and the (alpha, beta)- pre-Gruss inequality. Our results extend existing integral inequalities reported in the literature. Additionally, we discuss some applications of our results for continuous random variables (CRV, for short) with bounded probability density functions. Some new estimates are provided in this context, along with classical results obtained as special cases from our results.
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    NEW FRACTIONAL INTEGRAL EXTENSIONS FOR INEQUALITIES INVOLVING MONOTONE FUNCTIONS
    (Element D.O.O., 2024) Dahmani, Zoubir; Kaddar, Djamal; Sarikaya, Mehmet Zeki
    This paper extends classical results on integral inequalities involving monotone functions to the domain of Riemann-Liouville fractional integrals with positive arbitrary order a . By employing a unified framework, our approach provides a more generalized understanding of the interplay between monotonicity and integrability in the case of fractional integration. We review classical results, introduce Riemann-Liouville integrals, and establish the fractional integral extensions. Our main results are presented, with discussions on their applications, contributing to a broader comprehension of this type of inequalities in mathematical analysis and its applications. © 2025 Elsevier B.V., All rights reserved.
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    NEW GENERALIZATIONS OF HERMITE-HADAMARD TYPE INEQUALITIES
    (Erhan SET, 2023) Sarikaya, Mehmet Zeki
    In this study, we present a new generalization of the Hermite-Hadamard type inequalities for convex functions using a newly developed generalized an identity, which is rigorously proven. Moreover, we present new inequalities that are closely linked to both the left and right-hand side of the Hermite-Hadamard inequalities for Riemann and Riemann-Liouville fractional integrals. The results of this study build upon previous works and provide additional insights. © 2025 Elsevier B.V., All rights reserved.
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    New regular perturbation for a sequential random differential problem of Airy type
    (Univ Nis, Fac Sci Math, 2024) Fettouch, Houari; Dahmani, Zoubir; Sarikaya, Mehmet Zeki; Beddani, Hamid
    In this paper, we study a new problem of random differential equations of Airy type by means of the stochastic mean square theory. A new perturbation problem is introduced and some existence and uniqueness results for stochastic process solutions are established. At the end, an example is discussed in details.
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    ON GENERALIZED CONFORMABLE FRACTIONAL CALCULUS ON TIME SCALES WITH APPLICATION TO A FRACTIONAL NONLOCAL THERMISTOR PROBLEM
    (Georgian Natl Acad Sciences, 2025) Bendouma, Bouharket; Sarikaya, Mehmet Zeki
    In this paper, we give a new general definition of conformable fractional derivative and integral on time scales, and study some of their important classical properties. As an application, the existence of solutions for the conformable fractional nonlo cal thermistor problem on time scales is studied by using the Banach contraction principle and Schauder's fixed point theorem.
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    On Hermite-Hadamard type Inequalities for Proportional Caputo-Hybrid Operator
    (Prof. Dr. Mehmet Zeki SARIKAYA, 2023) Sarikaya, Mehmet Zeki
    In this study, we present a new generalization of the Hermite-Hadamard type inequalities for convex functions via proportional Caputo-hybrid operator. Also, we give some new inequalities for proportional Caputo-hybrid operator using a newly developed generalized an identity, which is rigorously proven. © 2024 Elsevier B.V., All rights reserved.
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    On Milne Type Inequalities For h-Convex Functions Via Conformable Fractional Integral Operators
    (Tsing Hua Univ, Dept Mathematics, 2025) Benaissa, Bouharket; Sarikaya, Mehmet Zeki
    In this study, Milne-type inequalities for h-convex functions involving conformable operators are established. In addition, new results are presented that generalize various inequalities known in the literature.
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    On Simpson Type Inequalities for Proportional Caputo-Hybrid Operator
    (Springer, 2025) Sarikaya, Mehmet Zeki
    In this article, we will start by presenting an identity that is crucial for the main result. Then, we will utilize this identity to derive Simpson’s integral inequality for the Proportional Caputo-Hybrid Operator. Additionally, we will provide some examples of special cases that arise from this inequality. © 2025 Elsevier B.V., All rights reserved.
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    On the generalized trapezoid and midpoint type inequalities involving Euler’s beta function
    (SINUS Association, 2023) Sarikaya, Mehmet Zeki; Kozan, Gizem
    The main object of this paper is to present some generalizations of fractional integral inequalities involving Euler’s beta function of Hermite-Hadamard type which cover the previously published result such as Riemann integral, Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral. © 2024 Elsevier B.V., All rights reserved.
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    On the Hermite-Hadamard's and Ostrowski's inequalities for the co-ordinated convex functions
    (Biska Bilişim, 2017) Erden, Samet; Sarikaya, Mehmet Zeki
    In this paper, we give new some inequalities of Hermite-Hadamard's and Ostrowski's type for convex functions on the co-ordinates defined in a rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the co-ordinates on the rectangle from the plane.
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    RECENT DEVELOPMENTS OF INTEGRAL INEQUALITIES OF THE HARDY-HILBERT TYPE
    (Erhan SET, 2024) Sarikaya, Mehmet Zeki; Bingöl, Mehmet Sabir
    Our aim in this study will be to obtain a new Hardy-Hilbert type of inequalities, taking into account the two studies by given Sulaiman and Wei-Lei. © 2025 Elsevier B.V., All rights reserved.
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    Refinements Jensen's Inequality and Some Their Applications
    (Mehmet Zeki SARIKAYA, 2024) Sarikaya, Mehmet Zeki
    This paper aims to present a new refinement of the Jensen inequality specifically for convex functions. Building on this refinement, the paper derives various related inequalities, with a particular focus on Bullen's inequality and Ostrowski's inequality. Furthermore, it explores practical applications of these derived inequalities in the context of mean inequalities, providing a deeper understanding and broader utility of these mathematical concepts.
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    Refinements Jensen’s Inequality and Some Their Applications
    (Prof. Dr. Mehmet Zeki SARIKAYA, 2024) Sarikaya, Mehmet Zeki
    This paper aims to present a new refinement of the Jensen inequality specifically for convex functions. Building on this refinement, the paper derives various related inequalities, with a particular focus on Bullen’s inequality and Ostrowski’s inequality. Furthermore, it explores practical applications of these derived inequalities in the context of mean inequalities, providing a deeper understanding and broader utility of these mathematical concepts. © 2024 Elsevier B.V., All rights reserved.
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    Simpson's quadrature formula for third differentiable and s-convex functions
    (Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarikaya, Mehmet Zeki
    This study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for various convexity cases.
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    Some weighted Hermite-Hadamard type inclusions based on interval-valued convex and co-ordinated convex mappings
    (Univ Nis, Fac Sci Math, 2024) Kara, Hasan; Sarikaya, Mehmet Zeki; Budak, Huseyin
    In this paper, we establish some Hermite-Hadamard inclusions for interval-valued convex functions and interval-valued co-ordinated convex functions by using interval-valued weighted function. The inclusions established in this work provide generalizations of some results given in earlier works. As special cases, we give some new weighted Hermite-Hadamard type inclusions involving logarithmic function.