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Öğe 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 ZekiIn 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.Öğe Chebyshev Type Inequalities for Generalized Stochastic Fractional Integrals(Amer Inst Physics, 2017) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Dahmani, ZoubirThe concept of comonotonic stochastic processes was introduced by Agahi and Yadollahzadeh. In this paper, we establish some Chebyshev type inequalities for comonotonic stochastic processes via generalized mean-square fractional integrals J(rho,lambda,a+;omega)(sigma) and J(rho,lambda,b-;omega)(sigma) which were introduced by Budak and Sarikaya.Öğe Genç Olguda Genel Durum Bozukluğu ve Bilinç Durum Değişikliği: Bonzai(2015) Ateş, Hakan; Dahmani, Zoubir; Kocaoğlu, Nazan; Konuk, İsmail DoğanYoğun bakım ünitelerinde takip ve tedavi edilen olguların bir kısmını bilinç durum değişiklikleri oluşturmaktadır. Bilinç durum değişikliği; alkol intoksikasyonu, endokrin bozukluklar, travma, serebrovasküler sorunlar, zehirlenmeler vb. gibi birçok nedene bağlı olabilir. Sentetik kannabinoid reseptör agonistlerinin elde edilmesi oldukça kolay ve ucuz olması nedeniyle son yıllarda genç yaş gurubu insan popülasyonunda kullanımı oldukça yaygınlaşmaktadır. Bu ajanlar esrar benzeri psikoaktif etkiler oluşturmaktadır. Kullanım sonrası değişken semptomlarla sağlık kuruluşlarına başvurulabilirler. Biz de bonzai kullanımı sonrası bilinç durum değişikliği nedeniyle yoğun bakım ünitesinde takip ve tedavi ettiğimiz olguyu paylaştık.Öğe (k, s)-Riemann-Liouville fractional integral and applications(Hacettepe Univ, Fac Sci, 2016) Sarıkaya, Mehmet Zeki; Dahmani, Zoubir; Kiriş, Mehmet Eyüp; Ahmad, FarooqIn this paper, we introduce a new approach on fractional integration, which generalizes the Riemann-Liouville fractional integral. We prove some properties for this new approach. We also establish some new integral inequalities using this new fractional integration.Öğe The (k, s, h)-Riemann-Liouville and the (k, s)-Hadamard Operators(Islamic Azad Univ, Shiraz Branch, 2022) Bezziou, Mohamed; Dahmani, Zoubir; Sarıkaya, Mehmet ZekiThis paper deals with new results on Gruss inequality by using recent fractional integral operators. In fact, based on the (k, s, h)-Riemann-Liouville and the (k, h) fractional operators, we establish several integral results. For our results, some very recent results on the paper: [A Gruss type inequality for two weighted functions. J. Math. Computer Sci., 2018.] can be deduced as some special cases.Öğe New integral inequalities for (R, ?)-fractional moments of continuous random variables(Publishing House of the Romanian Academy, 2018) Houas, Mohamed; Dahmani, Zoubir; Sarıkaya, Mehmet ZekiIn this paper, we establish new integral inequalities for continuous random variables. By introducing new concepts on fractional moments of continuous random variables, we generalize some interesting results of P. Kumar. Other fractional integral results are also presented. © 2018, Publishing House of the Romanian Academy. All rights reserved.Öğe New Operators for Fractional Integration Theory with Some Applications(Islamic Azad Univ, Shiraz Branch, 2018) Bezziou, M.; Dahmani, Zoubir; Sarıkaya, Mehmet ZekiIn this paper, we introduce new generalizations for the well konwn (k,s,h)-Riemann-Liouville, (k,s)-Hadamard and (k,s,h)-Hadamard fractional integral operators. We prove some of their properties. Then, using our proposed approaches, we establish some applications on inequalities.Öğe New results on symmetrized convex sequences(Element, 2024) Abdellaoui, Mohamed Amin; Mebarki, Houda; Dahmani, Zoubir; Sarıkaya, Mehmet ZekiIn this article, we establish new inequalities involving symmetrized convex sequences. The obtained results involve a new range of applications that contains the set of convex sequences. Some applications are given at the end of this paper.Öğe New W-weighted concepts for continuous random variables with applications(Aracne Editrice, 2017) Dahmani, Zoubir; Bouziane, Aboubakr Essedik; Houas, Mohamed; Sarıkaya, Mehmet ZekiNew concepts on fractional probability theory are introduced and some inequalities for the fractional w-weighted expectation and the fractional w-weighted variance of continuous random variables are obtained. Other fractional results related to the two orders fractional w-weighted moment are also established. Some recent results on integral inequality theory can be deduced as some special cases. At the end, some applications on the uniform random variable are given.Öğe A nonlocal multi-point singular fractional integro-differential problem of Lane-Emden type(Wiley, 2020) Gouari, Yazid; Dahmani, Zoubir; Sarikaya, Mehmet ZekiIn 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.Öğe 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 ZekiIn 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.Öğe A sequential fractional differential problem of pantograph type: existence uniqueness and illustrations(Scientific Technical Research Council Turkey-Tubitak, 2021) Belarbi, Soumia; Dahmani, Zoubir; Sarikaya, Mehmet ZekiIn this study, a new class of sequential fractional differential problems of pantograph type is introduced. New existence and uniqueness criteria for the existence and uniqueness of solutions are discussed. Some existence results using Darbo's fixed point and measure of noncompactness are also studied. At the end, two illustrative examples are discussed.Öğe SOME ESTIMATIONS ON CONTINUOUS RANDOM VARIABLES INVOLVING FRACTIONAL CALCULUS(Etamaths Publ, 2017) Dahmani, Zoubir; Khameli, Amina; Bezziou, Mohamed; Sarıkaya, Mehmet ZekiUsing fractional calculus, new fractional bounds estimating the w-weighted expectation, the w-weighted variance and the w-weighted moment of continuous random variables are obtained. Some recent results on classical bounds estimations are generalized.Öğe Some integral inequalities for (k, s) - Riemann-Liouville fractional operators(Taru Publications, 2018) Houas, Mohamed; Dahmani, Zoubir; Sarıkaya, Mehmet ZekiIn this paper, by using a new fractional integral approach of M.Z. Sarikaya et al., we establish new generalized fractional integral inequalities involving (k, s) - Riemann-Liouville integral operators. Some classical and non classical integral inequalities can be deduced as some special cases.Öğe A three fractional order jerk equation with anti periodic conditions(Univ Nis, 2023) Dahmani, Zoubir; Belhamiti, Meriem Mansouria; Sarikaya, Mehmed ZekiWe study a new Jerk equation involving three fractional derivatives and anti periodic conditions. By Banach contraction principle, we present an existence and uniqueness result for the considered problem. Utilizing Krasnoselskii fixed point theorem we prove another existence result governing at least one solution. We provide an illustrative example to claim our established results. At the end, an approximation for Caputo derivative is proposed and some chaotic behaviours are discussed by means of the Runge Kutta 4th order method.Öğe Two fractional order Langevin equation with new chaotic dynamics(Ankara Univ, Fac Sci, 2023) Belhamiti, Meriem Mansouria; Dahmani, Zoubir; Sarikaya, Mehmet ZekiIn the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theo-rem under a weak topology, and an illustrative example is then given. Further-more, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.Öğe Uniqueness of solutions, stability and simulations for a differential problem involving convergent series and time variable singularities(Rocky Mt Math Consortium, 2023) Gouari, Yazid; Dahmani, Zoubir; Belhamiti, Meriem Mansouria; Sarikaya, Mehmet ZekiWe study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series combined with Riemann-Liouville integrals. We prove an existence and uniqueness result for our problem. Some examples are given to illustrate the uniqueness result. The Ulam-Hyers stability for the problem is also studied. Then, thanks to some numerical techniques, that allow us to approximate the Caputo derivatives, and by using the Runge-Kutta method, we present a numerical study with some simulations to show more comprehension of the proposed examples.
