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Öğe Certain fractional inequalities via the Caputo Fabrizio operator(Univ Nis, Fac Sci Math, 2023) Qaisar, Shahid; Munir, Arslan; Budak, HüseyinThe Caputo Fabrizio fractional integral operator is one of the key concepts in fractional calculus. It is involved in many concrete and practical issues. In the present study, we have discussed some novel ideas to fractional Hermite-Hadamard inequalities within a Caputo Fabrizio fractional integral framework. The fractional integral under investigation is used to establish some new fractional Hermite-Hadamard inequalities. The findings of this study can be seen as a generalization and extension of numerous earlier inequalities via convex function. In addition, we demonstrate a few applications of our findings to special means of real numbers.Öğe Error Bounds for Fractional Integral Inequalities with Applications(Mdpi, 2024) Alqahtani, Nouf Abdulrahman; Qaisar, Shahid; Munir, Arslan; Naeem, Muhammad; Budak, HüseyinFractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite-Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo-Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite-Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.Öğe Generalizations of Simpson type inequality for (?, m)-convex functions(Univ Nis, Fac Sci Math, 2024) Munir, Arslan; Budak, Hüseyin; Faiz, Irza; Qaisar, ShahidSeveral scholars are interested in fractional operators with integral inequalities. Due to its characteristics and wide range of applications in science, engineering fields, artificial intelligence and fractional inequalities should be employed in mathematical investigations. In this paper, we establish the new identity for the Caputo-Fabrizio fractional integral operator. By utilizing this identity, the generalization of Simpson type inequality for ( alpha, m ) -convex functions via the Caputo-Fabrizio fractional integral operator. Furthermore, we also include the applications to special means, q -digamma functions, Simpson formula, Matrix inequalities, Modified Bessel function, and mind -point formula. These applications have given a new dimension to scholars.Öğe New approaches to corrected Euler-Maclaurin-type inequalities involving Riemann-Liouville fractional integrals for different function classes(Springer, 2025) Kara, Hasan; Hezenci, Fatih; Munir, Arslan; Budak, HuseyinThis paper investigates several Corrected Euler-Maclaurin-type inequalities for different function classes using Riemann-Liouville fractional integrals. The results, which are derived from special cases of theorems and illustrative examples, are subsequently presented. Furthermore, the authors have developed fractional Corrected Euler-Maclaurin-type inequalities for bounded functions. In addition, the research has acquired fractional Corrected Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, the study concludes with the derivation of fractional Corrected Euler-Maclaurin-type inequalities for functions of bounded variation.Öğe A New extension of Hermite Hadamard inequalities associating ψ-Hilfer fractional integral(Palestine Polytechnic University, 2025) Qayyum, Ather; Budak, H¨Useyin; Bat, Umut; Kara, Hasan; Munir, Arslan; Rathour, LaxmiFractional inequalities have been an essential topic in mathematics and have found applications in various domains. In this article, we established some new bounds (below and above) for mid-point type inequality and trapezoidal-type inequality for ψ-Hilfer- fractional integral by utilizing functions whose second derivatives are bounded. We also investigate some new generalization and extension of Hermite-Hadamard type inequalities for ψ-Hilfer fractional integrals for the functions having the condition: (Formula presented). © 2025 Elsevier B.V., All rights reserved.Öğe A NOTE ON SIMPSON 3/8 RULE FOR FUNCTION WHOSE MODULUS OF FIRST DERIVATIVES ARE s-CONVEX FUNCTION WITH APPLICATION(Kangwon-Kyungki Mathematical Soc, 2024) Munir, Arslan; Budak, Huseyin; Kara, Hasan; Rathour, Laxmi; Faiz, IrzaResearchers continue to explore and introduce new operators, methods, and applications related to fractional integrals and inequalities. In recent years, fractional integrals and inequalities have gained a lot of attention. In this paper, firstly we established the new identity for the case of differentiable function through the fractional operator (Caputo-Fabrizio). By utilizing this novel identity, the obtained results are improved for Simpson second formula-type inequality. Based on this identity the Simpson second formula-type inequality is proved for the s-convex functions. Furthermore, we also include the applications to special means.Öğe Novel generalized tempered fractional integral inequalities for convexity property and applications(Walter De Gruyter Gmbh, 2025) Kashuri, Artion; Munir, Arslan; Budak, Huseyin; Hezenci, FatihInequalities involving fractional operators have also been an active area of research. These inequalities play a crucial role in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, firstly we established two new identities for the case of differentiable convex functions using generalized tempered fractional integral operators. By utilizing these identities, some novel inequalities like Simpson-type, Bullen-type, and trapezoidal-type are proved for differentiable s-convex functions. Additionally, from the obtained results, several special cases of the known results for different choices of parameters are recaptured. Finally, some applications to q-digamma and modified Bessel functions are given.Öğe Some Caputo-Fabrizio fractional integral inequalities with applications(Univ Nis, Fac Sci Math, 2024) Qaisar, Shahid; Munir, Arslan; Naeem, Muhammad; Budak, HuseyinFractional calculus provides a significant generalization of classical concepts and overcomes the limitation of classical calculus in dealing with non-differentiability ff erentiability function. Implementing fractional operator to obtain new versions of classical outcomes is very intriguing topic of research in the mathematical analysis. The objective of the present study is to establish novel Hermite-Hadamard integral inequalities for twice differentiable ff erentiable function using Caputo-Fabrizio integral operator. In order to complete task, we start by demonstrating a new identity for Hermite-Hadamard inequality that serve as supporting result for our main finding. It has been observed that the obtained Hermite-Hadamard type inequalities have a relationship with previous results. In addition, we provide application to special means and graphical analysis to evaluate the accuracy of our results.Öğe Some new fractal Milne-type inequalities for generalized convexity with applications(Springer, 2025) Munir, Arslan; Budak, Huseyin; Kashuri, Artion; Hezenci, FatihFractals are of immense importance across various branches of mathematics, science, and integral inequalities, as their intricate, self-similar structures can model complex natural phenomena and enhance the precision of mathematical descriptions. In this article, we explore generalized Milne-type integral inequalities within the framework of generalized m-convex functions on fractal sets. To achieve this, we introduce a novel fractal integral identity involving differentiable generalized functions. Utilizing this new identity, we derive several contemporary fractal Milne-type integral inequalities and provide specific inequalities for bounded functions. Additionally, we offer illustrative examples and applications, including additional inequalities for generalized special means and various error estimates for the generalized Milne-type quadrature formula.Öğe Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function(Taylor & Francis Inc, 2024) Munir, Arslan; Vivas-Cortez, Miguel; Qayyum, Ather; Budak, Hüseyin; Faiz, Irza; Supadi, Siti SuzlinFractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for $s$s-convex function are obtained. By employing well-known inequalities such as H & ouml;lder's and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.Öğe Some New Improvements of Hermite-Hadamard Type Inequalities Using Strongly (s, m)-Convex Function with Applications(Univ Maragheh, 2025) Munir, Arslan; Budak, Huseyin; Kashuri, Artion; Faiz, Irza; Kara, Hasan; Qayyum, AtherThe trapezoidal-type inequalities are discovered in this study using the fractional operator, which produces powerful results. We established a general identity for Caputo-Fabrizio integral operators and the second derivative function. Using this identity new error bounds and estimates for strongly (s, m)-convex functions are obtained. Moreover, some novel trapezoidal-type inequalities are offered taking this identity into account using the known inequalities like Young, Jensen, Holder and power-mean inequalities. Finally, we present some applications for matrix inequality, estimation error regarding trapezoidal formulas and special means for real numbers.Öğe A study of Milne-type inequalities for several convex function classes with applications(Univ Nis, Fac Sci Math, 2024) Munir, Arslan; Qayyum, Ather; Budak, Huseyin; Faiz, Irza; Kara, Hasan; Supadi, Siti SuzlinFractional integral operators have indeed been the subject of significant research in various mathematical and scientific disciplines over the past few decades. The main aim of this article is to establish a new identity employing the Atangana Baleanu fractional integral operator for the case of differentiable functions. Moreover, we present several fractional Milne-type inequalities for bounded function by fractional integrals. Furthermore, we obtain fractional Milne-type inequalities for the case of Lipschitzian functions. Lastly, we explore applications related to special means, and quadrature formulas.Öğe A Study of Some New Hermite-Hadamard Inequalities via Specific Convex Functions with Applications(Mdpi, 2024) Junjua, Moin-ud-Din; Qayyum, Ather; Munir, Arslan; Budak, Hüseyin; Saleem, Muhammad Mohsen; Supadi, Siti SuzlinConvexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo-Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.
