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Approximating the Finite Mellin and Sumudu Transforms Utilizing Wavelet Transform
(Univ Nis, Fac Sci Math, 2020) Usta, Fuat; Budak, Huseyin; Sarikaya, Mehmet Zeki
In this study, some approximates for the finite Wavelet transform of different classes of absolutely continues mappings are presented using Wavelet transform of unit function. Then, with the help of these approximates, some other approximates for the finite Mellin and Sumudu transforms are given.
Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam-Hyers stability and travelling waves
(Springer Basel Ag, 2024) Bensassa, Kamel; Dahmani, Zoubir; Rakah, Mahdi; Sarikaya, Mehmet Zeki
In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the existence and uniqueness of solutions are proved by using two fixed point theorems. Some examples are discussed to illustrate the applications of the existence and uniqueness of solution results. Another main result on the Ulam-Hyers stability of solutions for the introduced system is also discussed. Some examples of stability are discussed. New travelling wave solutions are obtained for another conformable coupled system of beam type that has a connection with the first considered system. A conclusion follows at the end.
Bounds for the Error in Approximating a Fractional Integral by Simpson's Rule
(Mdpi, 2023) Budak, Hueseyin; Hezenci, Fatih; Kara, Hasan; Sarikaya, Mehmet Zeki
Simpson's rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann-Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson's inequalities is the first paper in the literature as a method.
FRACTIONAL HERMITE HADAMARD'S TYPE INEQUALITY FOR THE CO-ORDINATED CONVEX FUNCTIONS
(Inst Applied Mathematics, 2020) Tunc, Tuba; Sarikaya, Mehmet Zeki; Yaldiz, Hatice
In this paper, we consider the co-ordinated convex functions and obtain some Hermite-Hadamard type inequalities via Riemann-Liouville fractional integrals. For this purpose, we first prove an supplement al result for two variables. Using this auxiliary result, integral inequalities for the left-hand side of the fractional Hermite-Hadamard type inequality on the coordinates are derived. These represent can be viewed as a refinement of the previously known results.
FRACTIONAL HERMITE-HADAMARD-TYPE INEQUALITIES FOR INTERVAL-VALUED FUNCTIONS
(Amer Mathematical Soc, 2020) Budak, Huseyin; Tunc, Tuba; Sarikaya, Mehmet Zeki
In this paper, we define interval-valued right-sided Riemann-Liouville fractional integrals. Later, we handle Hermite-Hadamard inequality and Hermite-Hadamard-type inequalities via interval-valued Riemann-Liouville fractional integrals.
Fractional integral inequalities for generalized convexity
(Tbilisi Centre Math Sci, 2020) Kashuri, Artion; Ali, Muhammad Aamir; Abbas, Mujahid; Budak, Hiiseyin; Sarikaya, Mehmet Zeki
In this paper, we define a new class of functions called generalized phi-convex function. Several variants of Hermite-Hadamard type fractional integral inequalities are presented. This ideas and techniques used in this paper may open new avenues of research and motivate the reader to explore the application of generalized phi-convex functions in various branches of pure and applied sciences.
Hermite-Hadamard-type Inequalities for h-preinvex Interval-Valued Functions via Fractional Integral
(Springernature, 2023) Tan, Yun; Zhao, Dafang; Sarikaya, Mehmet Zeki
We present a comprehensive study on Hermite-Hadamard-type inequalities for interval-valued functions that are h-preinvex, using the Riemann-Liouville fractional integral. Our research extends and generalizes some existing results found in the literature. In addition, we provide accurate proofs for the main theorems originally derived by Srivastava et al. in their publication titled ''Hermite-Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators'' (Int. J. Comput. Int. Sys. 15(1):8, 2022). Finally, we illustrate our findings through a practical example to demonstrate the validity of our results.
Hermite-Hadamard-type inequalities for the interval-valued approximatelyh-convex functions via generalized fractional integrals
(Springer, 2020) Zhao, Dafang; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Huseyin; Sarikaya, Mehmet Zeki
In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called interval-valued approximatelyh-convex functions. We establish some inequalities of Hermite-Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302,2018and H. Budak et al. in Proc. Am. Math. Soc.,2019). We also discussed some special cases from our main results.
New generalization of Hermite-Hadamard type inequalities via generalized fractional integrals
(Univ Craiova, 2020) Budak, Huseyin; Ertugral, Fatma; Sarikaya, Mehmet Zeki
In this paper we obtain new generalization of Hermite-Hadamard inequalities via generalized fractional integrals defined by Sarikaya and Ertugral. We establish some midpoint and trapezoid type inequalities for functions whose first derivatives in absolute value are convex involving generalized fractional integrals.
New Hermite-Hadamard type inequalities on fractal set
(Semnan Univ, 2021) Tunc, Tuba; Budak, Huseyin; Usta, Fuat; Sarikaya, Mehmet Zeki
In this study, we present the new Hermite-Hadamard type inequality for functions which are h-convex on fractal set R-alpha (0 < alpha <= 1) of real line numbers. Then we provide the special cases of the result using different type of convex mappings.
Newton-type inequalities associated with convex functions via quantum calculus
(Univ Miskolc Inst Math, 2024) Luangboon, Waewta; Nonlaopon, Kamsing; Sarikaya, Mehmet Zeki; Budak, Huseyin
In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton -type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking q -> 1(-) . Finally, we give mathematical examples of convex functions to verify the newly established inequalities.
A nonlocal multi-point singular fractional integro-differential problem of Lane-Emden type
(Wiley, 2020) Gouari, Yazid; Dahmani, Zoubir; Sarikaya, Mehmet Zeki
In this paper, using Riemann-Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane-Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results.
On a fractional problem of Lane-Emden type: Ulam type stabilities and numerical behaviors
(Springer, 2021) Tablennehas, Kamel; Dahmani, Zoubir; Belhamiti, Meriem Mansouria; Abdelnebi, Amira; Sarikaya, Mehmet Zeki
In this work, we study some types of Ulam stability for a nonlinear fractional differential equation of Lane-Emden type with anti periodic conditions. Then, by using a numerical approach for the Caputo derivative, we investigate behaviors of the considered problem.
On Generalization of Midpoint and Trapezoid Type Inequalities Involving Fractional Integrals
(Islamic Azad Univ, Shiraz Branch, 2020) Sarikaya, Mehmet Zeki; Sonmezoglu, Sumeyye
In this paper, we first give a lemma for twice differentiable function to obtain trapezoid and midpoint inequalities. By using this lemma, we establish some inequalities for mapping whose second derivatives in absolute value are convex via Riemann-Liouville fractional integrals. These results generalize the midpoint and trapezoid inequalities involving Riemann-Liouville fractional integrals given in earlier studies.
On generalized fractional integral inequalities for twice differentiable convex functions
(Elsevier, 2020) Mohammed, Pshtiwan Othman; Sarikaya, Mehmet Zeki
In this article, some new generalized fractional integral inequalities of midpoint and trapezoid type for twice differentiable convex functions are obtained. In view of this, we obtain new integral inequalities of midpoint and trapezoid type for twice differentiable convex functions in a form classical integral and Riemann-Liouville fractional integrals. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable. (C) 2020 The Author(s). Published by Elsevier B.V.
On new generalized quantum integrals and related Hermite-Hadamard inequalities
(Springer, 2021) Kara, Hasan; Budak, Huseyin; Alp, Necmettin; Kalsoom, Humaira; Sarikaya, Mehmet Zeki
In this article, we introduce a new concept of quantum integrals which is called T-kappa 2(q)-integral. Then we prove several properties of this concept of quantum integrals. Moreover, we present several Hermite-Hadamard type inequalities for T-kappa 2(q)-integral by utilizing differentiable convex functions. The results presented in this article are unification and generalization of the comparable results in the literature.
On new refinements and generalizations of Q-Hermite-Hadamard inequalities for convex functions
(Rocky Mt Math Consortium, 2024) Alp, Necmettin; Budak, Huseyin; Sarikaya, Mehmet Zeki; Ali, Muhammad Aamir
We aim to prove generalized estimations for the q-Hermite-Hadamard inequality for convex functions using a parameter. By choosing this particular parameter, we show that our results reduce the previously obtained q-Hermite-Hadamard inequalities. We also present some new refinements of these q-Hermite- Hadamard inequalities. Furthermore, we establish a new lemma and, by using this lemma, we obtain some new quantum inequalities that generalize quantum midpoint and quantum trapezoid inequalities for convex functions.
On some Grüss-type inequalities via k-weighted fractional operators
(Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarikaya, Mehmet Zeki
In this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr & uuml;ss-type fractional integral inequalities. Furthermore, we establish and provide proofs for a set of inequalities that incorporate k-weighted fractional integrals.
On some inequalities for submultiplicative functions
(Springernature, 2021) Ali, Muhammad Aamir; Sarikaya, Mehmet Zeki; Budak, Huseyin; Zhang, Zhiyue
In this work, authors establish Hermite-Hadamard inequalities for submultiplicative functions and give some more inequalities related to Hermite-Hadamard inequalities. We also give new inequalities of Hermite-Hadamard type in the special cases of our main results.
On some new Hardy-type inequalities
(Wiley, 2020) Benaissa, Bouharket; Sarikaya, Mehmet Zeki; Senouci, Abdelkader
In this paper, we give some new types of the classical Hardy integral inequality by including a second parameter q and using weighted mean operators S-1 := (S-1)(g)(w) and S-2 := (S-2)(g)(w) defined by S-1(x) = 1/W(x) integral(x)(a) w(t)g(f(t))dt, S-2(x) = integral(x)(a) w(t)/W(t)g(f(t))dt, with W(x) = integral(x)(0) w(t)dt, for x is an element of(0,+infinity), where w is a weight function and g is a real continuous function on (0,+infinity).

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