Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Δ-Gronwall Dynamic Inequalities and Their Applications on Time Scales(Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Awrejcewicz, JanIn this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall-Bellman-Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation.Article Citation - WoS: 9Citation - Scopus: 9Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative(Asme, 2022) Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; Riaz, Muhammad BilalThis study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa-Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M-fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa-Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., beta = 0.1, the magnitude of truncated Mfractional derivative is greater whereas for increasing fractional orders, i.e., beta = 0.7 and beta = 0.99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.Article Citation - WoS: 17Citation - Scopus: 17Double Diffusive Magneto-Free Flow of Oldroyd-B Fluid Over a Vertical Plate With Heat and Mass Flux(Mdpi, 2022) Rehman, Aziz Ur; Awrejcewicz, Jan; Jarad, Fahd; Riaz, Muhammad BilalThe purpose of this research is to analyze the general equations of double diffusive magneto-free convection in an Oldroyd-B fluid flow based on the fundamental symmetry that are presented in non-dimensional form and are applied to a moving heated vertical plate as the boundary layer flow up, with the existence of an external magnetic field that is either moving or fixed consistent with the plate. The thermal transport phenomenon in the presence of constant concentration, coupled with a first order chemical reaction under the exponential heating of the symmetry of fluid flow, is analyzed. The Laplace transform method is applied symmetrically to tackle the non-dimensional partial differential equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid are presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations. Furthermore, some special cases for the movement of the plate are also studied.Article Citation - WoS: 2Citation - Scopus: 3(Δ Backward Difference )<sup> Backward Difference </Sup>-pachpatte Dynamic Inequalities Associated With Leibniz Integral Rule on Time Scales With Applications(Mdpi, 2022) Baleanu, Dumitru; Awrejcewicz, Jan; El-Deeb, Ahmed A.We prove some new dynamic inequalities of the Gronwall-Bellman-Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations.Article (γ,a)-Nabla Reverse Hardy-Hilbert Inequalities on Time Scales(Mdpi, 2022) Baleanu, Dumitru; Awrejcewicz, Jan; El-Deeb, Ahmed A.In this article, using a (gamma,a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extending several discrete inequalities and their corresponding continuous analogues. We say that symmetry plays an essential role in determining the correct methods with which to solve dynamic inequalities.Article Citation - Scopus: 1Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment(Tech Science Press, 2023) Baleanu, Dumitru; Ahmed, Nauman; Awrejcewicz, Jan; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Dayan, FazalThe application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters beta and delta, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.